- 73 Classwork 8.1
Name ________________________
Perform the indicated operation and simplify each as much as possible.
1)
24
7)
3 16 + 5 49
2)
5 24
8)
3 121 − 6 81
9)
9 x 2 + 2 49 x 2
3)
5 24x
3
2
4)
2 75w
5)
80wy 3
6)
5 9
10)
54w6 y 5
11)
15 • 6
12)
15 x • 6 x
- 74 13)
3 12 • 5 21
17)
Calculate to the nearest two decimal
5 + 37
places:
18)
Calculate to the nearest two decimal
7 − 2 43
places:
14)
14 x 3 • 35 x5
15)
6 49 • 3 169
19)
16)
6 49 + 3 169
20)
Calculate to the nearest two decimal
3 − 2 19
places:
6
places:
Calculate to the nearest two decimal
− 3 + (3) 2 − 4(5)(−6)
2(5)
- 75 Class work 8.1, 8.2, 8.3
Simplify as much as possible:
1.
Name ________________________
64
2. − 36x 2 y 4
16
25
3.
4.
3
27
5.
3
−8
6.
5
32
7.
3
x9
8.
4
x8 y12
9.
4
b11
y13
11. 12
12.
13.
32 x9 y 4
14. 5 90
15. −4bc 2 24b3c 6
16.
200
17.
50a 3b 4 c
18.
19. 5 72
20.
28 x 4 y 3 z 5
21. 12 x 4 y10
10.
22.
3
20 − 2 45 − 9 5
25. 6 2 − 9 5 − 4 5
45
98a 4b8c16
23. 4 12 + 6 3
24. 5 2 + 18 + 32
26. 3 2 + 50
27. 10 8 − 3 98 + 6 72
- 76 28. −5 12 ⋅ 2 2
(
)(
31. 3 + 5 2 5 + 2 2
34.
3
5
29.
)
(
3 2 6 − 4 15
(
)
(
30. 8 2 3 2 − 4 8
)(
32. 2 3 + 5 2 3 − 5
)
33.
1
2
15
5
35.
2
3
36.
)
37.
28a 3
7a
38.
6
20
39.
40.
14b6
20b7
41.
6
18
42.
1
7− 3
43.
1
6+ 3
44.
10
5 −9
45.
2
1+ 2
46.
7
5− 3
47.
3
3+5 3
48.
2 3
2 3 +3 2
8
y3
- 77 Classwork
Name ___________________________
Sec 8.4 Solving Radical Equations
Solve each equation using the square root property. Leave your answers in radical form simplified
as much as possible.
1.
y 2 = 45
2.
3x 2 = 108
3.
2 y 2 − 7 = 293
4.
(x − 6)2 = 49
5.
(w + 5)2 = 48
6.
5( x + 2) + 4 = 104
7.
4 p 2 + 11 = 60
8.
4( x + 11) = 160
9.
7x2 − 9 = 0
10.
Solve for r : πr 2 = 84
2
2
- 78 Solve each equation using the squaring property of equality.
11.
5x + 4
13.
4 − 3x
15.
2y − 3 = y − 9
17.
y +1 =
19.
5p =
=
x2 + 4
= 12
8
12.
2x + 9
14.
x =
3x + 10
16.
x =
7x
y2 + 5
18.
w−3 =
9 p 2 + 12
20.
Solve for t : d
=
5 − 11w
=
3t − 2
- 79 Classwork
Name ___________________________
Section 8.4 Applications of Radical Equations
Write all radical answers in simplified form and as a decimal rounded to two places.
1.
A square has area 80 square meters. Draw the square and label its sides. Find the length of a side
of the square. Write an equation for the area of the square. Solve your equation to find the solution to the
problem. Use your answer to find the perimeter of the square and the length of its diagonal.
Side (radical)
______________________
Side (decimal)
______________________
Diagonal (radical)
______________________
Diagonal (decimal)
______________________
Perimeter (radical)
______________________
Perimeter (decimal)
______________________
2.
The diagonal of a square is 12 meters long. Draw the square and label its diagonal and sides.
Find the length of a side of the square. Use the Pythagorean Theorem to write an equation. Solve your
equation to find the solution to the problem. Use your answer to find the area of the square and the
perimeter of the square.
Side (radical)
______________________
Side (decimal)
______________________
Area
______________________
Perimeter (radical)
______________________
Perimeter (decimal)
______________________
- 80 3.
The length of a rectangle is five times its width. The area of the rectangle is 280 square meters.
Draw the rectangle and label its length and width. Find the length and width of the rectangle. Write an
equation for the area of the rectangle. Solve your equation to find the solution to the problem. Use your
answers to find the perimeter of the rectangle and the length of its diagonal.
Width (radical)
_____________________
Width (decimal)
_____________________
Length (radical)
_____________________
Length (decimal)
_____________________
Perimeter (radical)
_____________________
Perimeter (decimal)
_____________________
Diagonal (radical)
_____________________
Diagonal (decimal)
_____________________
4.
The length of a rectangle is three times its width. The diagonal of the rectangle is 30 meters long.
Draw the rectangle and label its length, width and diagonal. Find the length and width of the rectangle.
Use the Pythagorean Theorem to write an equation. Solve your equation to find the solution to the
problem. Use your answers to find the area and the perimeter of the rectangle.
Width (radical)
_____________________
Width (decimal)
_____________________
Length (radical)
_____________________
Length (decimal)
_____________________
Perimeter (radical)
_____________________
Perimeter (decimal)
_____________________
Area
_____________________
- 81 Classwork
Sections 9.1 and 9.3 Solving Quadratic Equations
Name ____________________________
Quadratic Formula: to solve ax 2 + bx + c = 0 : x =
−b ± b 2 − 4ac
2a
Solve each equation. Write all radical answers in simplified form and as a decimal rounded to one place.
1)
x 2 = 280
2)
7
x − 9 = −30
8
3)
11 − 8( x − 5) = −2(3 x + 7)
4)
x 2 − 11x + 28 = 0
5)
( y − 9)2 = 100
6)
4 2
x = 40
5
7)
2m 2 + 9m − 5 = 0
8)
( 3x + 5 )
9)
3w 2 − 4w = 10
10)
0.08( x + 1) − 0.9(2 x + 3) = 3.4
2
= 100
- 82 11)
x + 5 2x − 7
=
8
5
12)
7 y 2 + 18 y + 8 = 0
13)
12 x 2 − 4 x = 0
14)
2
1
( y + 6) + (2 y − 10) = 9
3
5
15)
9w 2 − 15 = 0
16)
x −5 =
17)
x 2 = 13x
18)
3t 2 − 8 = 5t
19)
1
1
6
+
=
x x+3 7
20)
(x + 1)2 + (x − 4)2 = 21
2
x
3
- 83 Classwork
Section 9.4 Applications of Quadratic Equations
Write all answers as a decimal rounded to two places.
Name ________________________
1.
A rectangle has length five more than three times its width. The area of the rectangle is 65 square
meters. Find the length, width and perimeter of the rectangle. Draw the rectangle and label its length and
width. Write an equation for the area of the rectangle. Solve your equation to find the solution to this
problem.
Width
____________________
Length
____________________
Perimeter
____________________
2.
The length of a rectangle is 7 more than twice its width. A 3 foot border is added all the way
around the rectangle. The area of the new larger rectangle is 140 square feet. Find the length, width and
perimeter of the new larger rectangle. Draw the rectangle and label its length, width and the border.
Write an equation for the area of the rectangle. Solve your equation to find the solution to this problem.
Width
____________________
Length
____________________
Perimeter
____________________
3.
Mary has 120 feet of fencing to build a rectangular pig pen. She would like the area to be 540
square feet. Find the length and width of the pen. Draw the pen. Write an equation for the area of the
pen. Solve your equation to find the solution to this problem.
Width
____________________
Length
____________________
- 84 4.
One leg of a right triangle is 5 inches longer than the other leg. The hypotenuse of the triangle is
26 inches. Find the length of the legs of the triangle. Then find the area and perimeter of the triangle.
Draw the triangle and label the legs. Use the Pythagorean Theorem to write an equation. Solve the
equation to find the solution to the problem.
Leg a
____________________
Leg b
____________________
Perimeter
____________________
Area
____________________
5.
The length of a rectangle is 7 feet shorter than its width. It diagonal is 28 feet. Find the
dimensions of the rectangle. Draw the rectangle and label its length, width and diagonal. Use the
Pythagorean Theorem to write an equation. Solve your equation to solve the problem. Then find the area
and the perimeter of the rectangle.
Width
____________________
Length
____________________
Perimeter
____________________
Area
____________________
6.
Together Kelly and Tyler can paint the living room in eight hours. Working alone Tyler can paint
the living room in three hours more than it takes Kelly working alone. How long will it take each of
them, working alone, to paint the living room? Write an equation and use it solve the problem.
- 85 Classwork
Name __________________________________
Section 9.4 More Quadratic Applications
Write all answers as a decimal rounded to two places.
1.
A rectangle has length 6 more than five times its width. The area of the rectangle is 172 square
meters. Find the length, width, and perimeter of the rectangle. Draw the rectangle and label its length
and width. Write an equation for the area of the rectangle. Solve your equation to find the solution to the
problem.
Width
________________________
Length
________________________
Perimeter
________________________
2.
The length of a rectangle is 9 feet shorter than its width. Its diagonal is 37 feet. Find the
dimensions of the rectangle. Then find its area and perimeter. Draw the rectangle and label its length,
width and diagonal. Use the Pythagorean Theorem to write an equation involving the length, width and
diagonal. Solve your equation to find the solution to this problem.
Width
_______________________
Length
_______________________
Perimeter
_______________________
Area
_______________________
- 86 3.
The length of a rectangle is 5 more than three times its width. A 2 foot border is added all the way
around the rectangle. The area of the new larger rectangle is 80 square feet. Find the length, width and
perimeter of the new larger rectangle. Draw the rectangle and label its length, width and the border.
Write an equation for the area of the rectangle. Solve your equation to find the solution to this problem.
Width
______________________
Length
______________________
Perimeter
______________________
Area
______________________
4.
Together Jon and Dylan can mow the lawn in 12 hours. (It’s a very large lawn.) Working alone,
Dylan can mow the lawn in four hours more than it takes Jon working alone. How long will it take each
of them, working alone, to mow the lawn? Write an equation and use it to solve the problem.
- 87 ◊Area and Circumference of Circles
The parts of a circle are the center, radius, diameter, and circumference. The early Greeks and
Babylonians, circa 1000 B.C., discovered that the circumference divided by the radius is always the same
number. The Greeks used one of their letters pi ( π ) for as a name for the ratio. So, according to the
C
Greeks,
=π .
D
Mathematician have used various numbers as an approximation for π over the centuries. The following
is a summary of some the different numbers used for π.
Culture
Egyptian
Time Used
1650 B.E.
Greeks
(Archimedes)
Greeks
(Ptolemy)
Chinese
240 B.E.
150 A.E.
489 A.E.
Hindu
(Aryabahata)
530 A.E.
French
(Viete)
1579 A.E.
Abraham Sharp
1699 A.E.
Rutherford
1841 A.E.
Army Ballistic
Research
Laboratories
Central
Intelligence
Agency
1949 A.E.
1984 A.E.
Number Used
4
⎛4⎞
⎜ ⎟
⎝3⎠
223
22
<π <
71
7
377
120
355
113
62,832
20, 000
Decimal Equivalent
3.160
3.1408 < π < 3.1429
3.14166666…
3.1415929…
3.1416
3.141592654
Correct to nine
decimal places.
π correct to 71
decimal places
π correct to 208
decimal places
π correct to 2037
decimal places
π correct to 2 billion
decimal places
For a better history of π see Introduction to the History of Mathematics by Howard Eves. According to a
mathematical handbook π is 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 correct
22
to fifty decimal places. For our purposes, we will use either the letter π , 3.14, or
. We will use
7
π when asked to put the answer in π form. Use 3.14 when the radius or diameter is given in whole or
22
decimal form. Use
when the radius or diameter is given in fraction form.
7
- 88 ◊Area and Circumference of Circles
The formula for finding the area of a circle is A = π r 2 . The formula for finding the circumference of a
circle is C = Dπ or C = 2π r . Like the formulas for the area of triangles and quadrilaterals, it is wise to
memorize the two formulas.
Example 1: Find the area of a circle, if the diameter is 25.80cm.
Solution: Since the radius is one-half of the diameter, r=12.90. So,A=(3.14)(12.9)2=522.5274
Or rounded to two decimal places 522.53 cm2.
56
in.
3
1
⎛ 56 ⎞ 112
⎛ 112 ⎞ ⎛ 22 ⎞ ⎛ 112 ⎞ 352
and C = π ⎜
= 117 in.
Solution: D = ( 2 ) ⎜ ⎟ =
⎟ = ⎜ ⎟⎜
⎟=
3
3
3
⎝ 3 ⎠
⎝ 3 ⎠ ⎝ 7 ⎠⎝ 3 ⎠
Example 2: Find the Circumference of a circle, if r=
Example 3: Find C in π form, if D=15.
Solution: C = Dπ = 15π
Example 4: Find the Area in π form, if C=20π.
Solution:
Since C=Dπ and C=20π, then Dπ=20π and then D=20 and r=10. So A=π(10)2=100π.
Example 5: Find the Circumference in π form, if A=121π.
Solution: Since A=πr2 and A=121π, then πr2=121π. So, r2=121 and r=11. Then, D=22 and C=22π.
- 89 Classwork
Area and Circumference of Circles
Circle of radius r:
r
Name ____________________________
Area
A = πr 2
Circumference
C = 2πr
Write your answers in terms of π and as a decimal rounded to two places.
1)
A circle has radius 12 meters.
a)
2)
Find its circumference.
b)
Find its area.
Find its circumference.
b)
Find its area.
b)
Find its area.
b)
Find its area.
A circle has circumference 20π inches.
a)
5)
Find its area.
A circle has diameter 12 inches.
a)
4)
b)
A circle has radius 15.8 meters.
a)
3)
Find its circumference.
Find its radius.
A circle has circumference 34 meters.
a)
Find its radius.
- 90 6)
A circle has circumference 4π 5 inches.
a)
7)
b)
Find its area.
b)
Find its circumference.
b)
Find its circumference.
A circle has area 25π square inches.
a)
8)
Find its radius.
Find its radius.
A circle has area 60 square inches.
a)
Find its radius.
9)
Find the area of the square in the figure below. The circumference of the circle is 18π
inches.
10)
Find the area of the square in the figure below. The area of the circle is 36π square
inches.
- 91 ◊ Special Triangles
Three special triangles consistently arise in math classes up to and including calculus. The properties of these
triangles are important to learn and memorize so that later work can be done with speed. The triangles are
equilateral, isosceles right, and 30-60-90 triangles.
The equilateral triangle has three congruent sides and therefore has three congruent angles of 600. An angle
bisector of an angle cuts the triangle in half and is also perpendicular to a side.
2s
s 3
s
2s
s
So, if a side of the equilateral triangle is 2s, the base is cut in half with each part being s long. The altitude must be
s 3 long, since a right triangle is formed with a leg of s and hypotenuse of 2s. An additional property for the
equilateral triangle is as follows.
If the side of an equilateral triangle is 2s the altitude is s 3 . Also, the angles the triangle halves are 300, 600, and
900. So, the 30-60-90 triangle can be summarized below.
30-60-900 Triangle
300
s 3
2s
600
s
Example 1: If the hypotenuse of a 30-60-90 triangle is 20, find the other sides.
Solution: The shortest leg is
20
20
= 10 and the longest leg is
3 = 10 3 .
2
2
Example 2: If the longest leg of a 30-60-90 triangle is
Solution: The longest leg is
hypotenuse is 2s or 30.
15 3 , find the other leg and the hypotenuse.
s 3 long. So, s 3 = 15 3 and solving s=15. So, the shortest leg is 15 and the
Example 3: If the longest leg is
8 15 , find the shortest leg and the hypotenuse.
- 92 ◊ Special Triangles
Solution: Since using the triangle above
3 . So,
s 3 = 8 15 , s can be found by dividing both sides of the equation by
s 3 8 15
=
or s = 8 5 and the shortest side is 8 5 . The longest side is then 2(8 5) = 16 5 .
3
3
Isosceles Right Triangle
An isosceles right triangle has two congruent legs. And since the triangle is isosceles, the acute angles are
congruent. Therefore, the angles of an isosceles right triangle are 45-45-900. If one of the legs is s long and the
hypotenuse is h long, then s2+s2=h2. Solving for h.
2s 2 = h 2
2s 2 = h
s 2=h
The above properties of the isosceles right triangle are summarized in the figure below.
450
s 2
s
450
s
Example 1: One of the legs of an isosceles triangle is 15. Find the other leg and hypotenuse.
Solution: The second leg is the same length 15. The hypotenuse is 15 2 .
Example 2: The hypotenuse of an isosceles triangle is 30. Find the length of the legs.
Solution: Using the triangle above, if s 2 = 30 , then solving for s will give then leg length.
s 2 = 30
s 2 30
=
2
2
s=
30 30
2 30 2
=
•
=
2
2
2
2
s = 15 2
So, the legs are both 15 2
- 93 Classwork
Special Triangles
Name ________________________________
Given the following side of a 30-60-900 triangle, sketch the triangle and find the other sides. Then find the area and
perimeter of each triangle. Leave your answers in radical form, simplified as much as possible.
1. Shortest leg: 40
2. Shortest leg: 6
Area
_______________
Area
_______________
Perimeter
_______________
Perimeter
_______________
3. Hypotenuse: 80
4. Hypotenuse: 16 3
Area
_______________
Area
_______________
Perimeter
_______________
Perimeter
_______________
5. Longest leg: 5 3
6. Longest leg: 21
Area
_______________
Area
_______________
Perimeter
_______________
Perimeter
_______________
Directions: Given the following side in an isosceles right triangle, sketch the triangle and find the remaining sides.
Then find the area and perimeter of each triangle.
8. Leg: 2 5
7. Leg: 7
Area
_______________
Area
_______________
Perimeter
_______________
Perimeter
_______________
9. Hypotenuse: 5 2
10. Hypotenuse: 4 6
Area
_______________
Area
_______________
Perimeter
_______________
Perimeter
_______________
- 94 Find x, y, and z in the triangles below.
11.
12.
450
9
300
z
450
x
45
0
x
600 y
300
z
y
0
600 6
45
13. If a square has a side of 12 inches, find the length of the diagonal.
14. If the diagonal of a square is 20 cm, find the length of a side to the nearest tenth cm.
15. If an equilateral triangle has an altitude of 8 3 , find its area.
16. Find the altitude of the isosceles triangle below.
12cm
1200
12cm
- 95 LS 10A Review for Exam 4
Name _____________________________
Simplify each radical as much as possible:
1.
2.
3.
3 18 + 4 50
6.
14
7
7.
(2
8.
4
3+ 2 6
5 20 − 3 45 − 80
10 (2 5 + 3 15 )
5 −7
)(
4.
26 − 338
39
9.
5+3 7
1− 2 7
5.
(9 − 5 )(9 + 5 )
10.
3 y 198 y 7
5 +9
)
- 96 Solve each equation.
16.
2t 2 = 8t + 2
11.
z 2 = 75
12.
(5 x − 2) 2 = 16
17.
t 2 + 36 = −13t
13.
(7 x + 3)2 = 18
18.
25w 2 = 121
14.
x 2 − 11x + 10 = 0
19.
81y 2 − 1 = 0
15.
5 y2 − 6 y = 3
20.
a = 5a − 4
- 97 -
21.
3x − 2 = 4
For the following applications, write all radical
answers in simplified form and as a decimal
rounded to two places.
22.
y = 8y
23.
w + 2 = 10 + 9 w
24.
x 2 − 7 = 11
25.
The diagonal of a rectangle is 18 feet.
The length is seven times its width. Draw the
rectangle and label its diagonal and sides. Use
the Pythagorean Theorem to write an equation
to find the width of the rectangle. Use your
answer to find the length of the rectangle, its
area and its perimeter.
26.
The length of a rectangle is four times
its width. The area of the rectangle is 180
square meters. Draw the rectangle and label its
length and width. Find the length and width of
the rectangle. Write an equation for the area of
the rectangle and use it to solve the problem.
Then find the perimeter of the rectangle and the
length of its diagonal.
- 98 -
27.
A rectangle has length two more than
three times its width. The area of the rectangle is
90 square meters. Find the length and width of
the rectangle. Draw the rectangle and label its
length and width. Write an equation for the area
of the rectangle. Solve your equation to find the
solution to this problem. Then find the perimeter
of the triangle and the length of its diagonal.
28.
29.
One leg of a right triangle is 7 inches
longer than the other leg. The hypotenuse of the
triangle is 38 inches. Find the length of the legs
of the triangle. Draw the triangle and label the
sides. Use the Pythagorean Theorem to write an
equation. Solve the equation to find the length
of the legs. Then use your answers to find the
perimeter and area of the triangle.
Solve the equation:
(x − 1)
2
+ ( x + 3) = 65
2
30.
The perimeter of a square is 72 meters.
Find the length of each side of the square. Write
an equation for the perimeter of the square.
Solve the equation to find the length of a side of
the square. Then find the area of the square and
the diagonal of the square.
- 99 31.
The diagonal of a square is 18 meters
long. Draw the square and label the diagonal.
Find the length of a side. Use the Pythagorean
Theorem to write an equation. Solve the
equation to find the length of a side of the
square. Then find the area and the perimeter of
the square.
34.
A circle has circumference 28 meters.
Find its radius. Find its area.
35.
A circle has area 49π square meters.
Find its radius. Find its circumference.
32.
A circle has diameter 30 inches. Find its
circumference. Find its area.
33.
A circle has circumference 28π inches.
Find its radius. Find its area.
36.
A circle has area 49 square meters. Find
its radius. Find its circumference.
- 100 37.
The shortest leg of a 30 − 60 − 90 0
triangle is 5 inches. Draw the triangle and label
the angles and sides. Find the length of the other
leg and the hypotenuse. Find the perimeter and
area of the triangle.
38.
The hypotenuse of a 30 − 60 − 90 0
triangle is14 feet. Draw the triangle and label
the angles and sides. Find the length of the two
legs. Find the perimeter and area of the triangle.
39.
The longest leg of a 30 − 60 − 90 0
triangle is 17 3 feet. Draw the triangle and
label the angles and sides. Find the length of the
other leg and the hypotenuse. Find the perimeter
and area of the triangle.
40.
Together Ally and Lauren can paint the
living room in twelve hours. Working alone
Ally can paint the living room in four hours
more than it takes Lauren working alone. How
long will it take each of them, working alone, to
paint the living room? Write an equation and
solve it. Round your answers to the nearest two
decimal places.
- 101 Answers to Review for Exam 4
1.
29 2
2.
−3 5
18.
±
11
5
19.
±
1
9
3.
10 2 + 15 6
20.
1 or
4.
2− 2
3
21.
6
5.
76
22.
0 or 8
6.
2 7
23.
− 1 or
7.
− 53 + 11 5
24.
± 128 = ±8 2
8.
− 12 + 8 6
15
9.
− 47 − 13 7
27
10.
9 y 4 22 y
11.
±5 3
12.
6
5
or
25.
6
x 2 + (7 x ) = 18 2
2
2
5
−
4
9 2
ft ≈ 2.55 ft
5
63 2
l=
ft ≈ 17.82 ft
5
144 2
P=
ft ≈ 40.73 ft
5
A = 45.36 square feet
x=
26.
4 w 2 = 180
−3±3 2
7
P = 30 5 m ≈ 67.08 m
14.
10 or 1
d = 765 = 3 85 m = 27.66 m
15.
6 ± 96 3 ± 2 6
=
10
5
16.
4 ± 20
= 2± 5
2
17.
− 4 or
13.
w = 3 5 m ≈ 6.71 m
−9
w(3w + 2) = 90
− 2 ± 1084 − 1 ± 271
=
≈ 5.15 m
6
3
l ≈ 17.45
P = 45.2 m
d = 18.19 m
w=
27.
- 102 -
28.
− 4 ± 456 − 2 ± 114
=
4
2
≈ 4.34 or − 6.34
x=
35.
36.
29.
2
− 14 ± 11,356 − 7 ± 2839
=
≈ 23.14 in
4
2
other leg is 30.14 in
P = 91.28 in
A = 348.72 square inches
30.
s = 18 m
A = 324 m2
d = 18 2 m
37.
long leg 5 3 in
hypotenuse 10 in
Perimeter (15 + 5 3 ) in
25
Area
3 in 2
2
38.
31.
long leg 7 3 ft
short leg 7 ft
s=9 2 m
A = 162 m 2
Perimeter (21 + 7 3 ) ft
49
Area
3 ft 2
2
P = 36 2 m
32.
C = 30π ≈ 94.2 inches
A = 225π ≈ 706.5 in 2
r ≈ 3.95 m
C ≈ 24.81 m
x 2 + ( x + 7 ) = 38 2
x=
r =7m
C = 14π ≈ 43.96 m
39.
short leg
33.
hypotenuse 34 ft
r = 14 in
Perimeter
A = 196π ≈ 615.44 in 2
Area
34.
r ≈ 4.46 m
A ≈ 62.46 m 2
17 ft
(51 + 17 3 ) ft
289
3 ft 2
2
40.
1
1
1
+
=
x x + 4 12
20 + 592
x=
= 10 + 4 37 ≈ 22.17 hrs
2
Lauren 22.17 hours
Ally 26.17 hours