Student: _____________________
Date: _____________________
Instructor: TODD CONKLIN
Course: 2nd Hour Math
Assignment: Stretching and Shrinking
Test B Math
1. The scale drawing of the truck is 13 inches long. What is the actual length of the​ truck? 1 inch=1.6 feet
The gridlines are spaced 1 inch apart.
The actual length of the truck is
feet.
2. To the nearest​ millimeter, a cell phone is 86 mm long and 40 mm wide. What is the ratio of the width to the​ length?
The ratio of the width to the length is
. ​(Type the ratio as a simplified​ fraction.)
3. Find the unknown side lengths in similar triangles PQR
and ABC.
Q
B
25
a
15
9
R
b
P
A
12
C
a=
​(Simplify your answers. Type an integer or a​ fraction.)
b=
​(Simplify your answers. Type an integer or a​ fraction.)
4. The scale of a map is 1 cm = 76 km. What is the actual distance between two towns that are 3 cm apart on the​ map? The distance between the two towns is
5.
km.
The scale drawing is of a backyard tennis court. The scale is 1 cm = 2 m.
What is the actual area of the tennis​ court?
width
4.5 cm
length
12 cm
The actual area of the tennis court is
m2 .
6. Flooring How many square feet of flooring is needed to
cover the entire living room ​floor?
In the living room​,
square feet of flooring
is needed to cover the entire floor.
1 inch=3 feet
The gridlines are spaced 1 inch apart.
7.
The pair of figures to the right are similar. The area of one figure is given.
Find the area of the other figure to the nearest whole number.
Area of smaller parallelogram = 15 ft
2
3 ft
The area of the larger parallelogram is
​(Round to the nearest whole number as​ needed.)
2
ft .
8. The figures shown are similar. Find the lengths of​ x, y, and
z.
The length of side x is
​(Type an integer or a​ decimal.)
.
The length of side y is
​(Type an integer or a​ decimal.)
.
The length of side z is
​(Type an integer or a​ decimal.)
.
21 ft
y
x
12
z
32
29
16
29
9.
Use similar triangles and a proportion to find the length of the lake
shown here.
​(Hint: The side 100 m long in the smaller triangle corresponds to side
of 100 m + 120 m = 220 m in the larger​ triangle.)
50 m
100 m
120 m
220 m
n=
m
10. A triangle is formed by the​ building's height
and shadow. Another triangle is formed by
the​ flagpole's height and shadow. Using the
following​ diagram, find the height of the
building.
20 ft
24 ft
The height of the building is
11. If
ABC and
feet.
PQR are similar​ triangles, find QR and PR.
B
Q
40
24
A
32
27
C
R
P
QR =
PR =
12. Find the unknown lengths in the pair of similar triangles.
B
Q
18 in.
b
30 in.
R
A
12 in.
22 in.
a
C
The length of AC is
in.
The length of RQ is
in.
P
2 ft
13. Given that the pair of triangles is​ similar, find the
unknown length of the side labeled with a variable.
The unknown length is
x
15
100°
100°
9
13
​unit(s).
14. Find the unknown lengths in the pair of similar triangles.
​(Triangles are not drawn to scale. Assume corresponding
sides are in the same position within each​ triangle.)
a=
cm ​(Simplify your​ answer.)
b=
cm ​(Simplify your​ answer.)
8 cm
8 cm
5.5 cm
b
15. List the pairs of congruent angles and the extended proportion that relates
the corresponding sides for the similar triangles ΔKLM and ΔHIJ.
a
4 cm
H
J
I
K
L
M
List the pairs of congruent angles.
∠K is congruent to ∠
∠
.
​, ∠L is congruent to ∠
​, and ∠M is congruent to
Write the extended proportion that relates the corresponding sides for the similar triangles.
HI
=
HJ
=
IJ
1
2
16.
ABC and
XYZ are similar. Name the corresponding sides and angles.
A
X
B
C Z
Y
Name the corresponding side.
AB and
​(Type two vertices in the correct​ order.)
Name the corresponding angle.
∠A and ∠
​(Type a​ vertex.)
Name the corresponding side.
AC and ​(Type two vertices in the correct​ order.)
Name the corresponding angle.
∠B and ∠
​(Type a​ vertex.)
Name the corresponding side.
BC and ​(Type two vertices in the correct​ order.)
Name the corresponding angle.
∠C and ∠
​(Type a​ vertex.)
17.
The two triangles are similar. The smaller triangle has sides 6 ​inches,
7 ​inches, and 14 inches. The 14​-inch side on the smaller triangle
corresponds to a side of 25 inches of the larger triangle. What is the
perimeter of the larger​ triangle?
6
25
14
7
P≈
in ​(Round to the nearest​ tenth.)
18.
The areas of two similar figures are in the same ratio as the square of
the ratio of two corresponding sides. The two geometric figures are
similar. Find the unknown area.
2
A=342 yd
7 yd
5 yd
A=?
2
The unknown area is approximately
yd .
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)
19. Find the unknown side lengths in similar triangles PQR
and ABC.
Q
B
55
a
30
R
b
P
a=
​(Simplify your answers. Type an integer or a​ fraction.)
b=
​(Simplify your answers. Type an integer or a​ fraction.)
20. Use similar triangles to solve. A person who is 6 feet tall
is standing 108 feet from the base of a​ tree, and the tree
casts a 117 foot shadow. The​ person's shadow is 9 feet
in length. What is the height of the​ tree?
6 ft
108 ft
ft
9 ft
A
50
40
C
1. 20.8
2. 20
43
3. 15
20
4. 228
5. 216
6. 72
7. 735
8. 21.75
24
21.75
9. 110
10. 240
11. 45
36
12. 33
20
13. 10
14. 4
11
15. H
I
J
KL
KM
LM
16. XY
X
XZ
Y
YZ
Z
17. 48.2
18. 174.5
19. 33
44
20. 78