©TeeJay Publishers
General Homework for Book 3G
Ch 13 - Pythagoras
Pythagoras
Homework
Chapter 13
Exercise 1
1.
2.
3.
Find, without a calculator, the value of :(a) 42
(b)
32
(c)
72
(d)
102
(e) 92
(f)
12
(g)
82
(h)
62
Use a calculator (if you need to) to find the values of :(a)
132
(b)
182
(c)
212
(d)
302
(e)
452
(f)
602
(g)
752
(h)
1022
Calculate the areas of the following squares :(a)
(b)
(c)
11 m
22 mm
25 cm
4.
Calculate the area of this shape consisting of 5 squares.
The large one has sides 16 centimetres and 4 small
squares have sides 7 centimetres.
5.
Calculate the shaded area of this
shape here made from cutting a
small square hole from a larger square.
8m
13 m
this is Chapter Thirteen
page 72
©TeeJay Publishers
General Homework for Book 3G
Ch 13 - Pythagoras
Exercise 2
1.
Without using a calculator, write down :(a)
2.
16
(b)
25
(c)
In this question, you should use the
(a)
3.
81
(b)
225
49
(d)
64
button on your calculator to find :-
(c)
289
(d)
3600
(e)
1 ⋅ 96
Use your calculator to find these and round your answer to one decimal place :(a)
26
(b)
43
(c)
134
(d)
1700
This square shown has an area of 69 cm2
4.
Calculate the length of one of its sides (to 1 decimal place).
5.
The TOTAL area of this shape which
consists of two squares is 74 cm2.
The lengths of the sides of the big square are 7 cm.
(e)
69
cm2
74
7 cm
6 ⋅ 88
cm2
Calculate the length of each side of the small square.
7 cm
Exercise 3
1.
The three sides of this right angled triangle are 3 cm and 4 cm and 5 cm.
€
(a) Write down the values of 32 , 4 2 and 52 .
2
(b)
5 cm
2
Find the value of 3 + 4 .
4 cm
(c) € Check that 32 + 4 2 = 52 .
2.
The three sides of this right angled triangle are 12 cm and 16 cm and 20 cm.
Write down the values of 122 , 162 and 202 .
(a)
(b)
(c)
3.
3 cm
€
€
Find the value of 122 + 162 .
Check that 122 + 162 = 202 .
20 cm
16 cm
12 cm
The three sides of this right angled triangle are 16 cm, 30 cm and 34cm.
(a)
Write down the values of 162 , 302 and 34 2 .
(b)
Find the value of 162 + 302 .
(c)
€
Check that 162 + 302 = 34 2 .
this is Chapter Thirteen
34 cm
16 cm
page 73
30 cm
©TeeJay Publishers
General Homework for Book 3G
Ch 13 - Pythagoras
Exercise 4
1.
2.
Copy this working and show how to calculate the
length of the hypotenuse (c) :=>
c 2 = a 2 + b2
=>
c2 = 72 +
=>
c 2 = 49 + ? = ?
=>
c =
?
c
5 cm
b
?2
7 cm
a
= ? cm
Use Pythagoras’ Rule to calculate the hypotenuse in each of these triangles :(a)
7·5 cm
4 cm
(b)
(c)
c
c
c
c
15 cm
12 cm
20 cm
(d)
3·5 cm
(e)
(f)
11 cm
17 cm
c
6 cm
6·2 cm
c
c
12 cm
13·5 cm
Exercise 5
1.
Calculate the length of each side to two decimal places. (watch the units)
(a)
3 mm
8 mm
(b)
(c)
hm
31 cm
h mm
18 cm
5·6 m
h cm
3·1 m
cont’d ....
this is Chapter Thirteen
page 74
©TeeJay Publishers
(d)
General Homework for Book 3G
(e)
11·2 mm
Ch 13 - Pythagoras
(f)
53 m
8·3 mm
h mm
hm
h cm
15·5 cm
12·7 cm
29 m
2.
A strip of wood rests with its top
on the rim of a mug.
str
ip
18 cm
Calculate the length of the strip
of wood.
of
wo
od
24 cm
3.
A hot air balloon is tethered to the ground by
two ropes.
The shorter rope is vertical.
lon
shorter
ge
rr
rope
52 m
op
e
Calculate the length of the longer rope.
54 m
4.
x cm
Calculate the length of the sloping
side in this figure, (marked x).
12 cm
(hint :- look for the right angled triangle)
10 cm
16 cm
this is Chapter Thirteen
page 75
©TeeJay Publishers
General Homework for Book 3G
Ch 13 - Pythagoras
Exercise 6E
Calculate the length of the smaller side each time here :–
(a)
(b)
20 cm
13 cm
30 mm
b mm
a cm
2.
The wing of an aeroplane is in
the shape of a right angled triangle.
Calculate the length of the small
edge of the wing.
9·5 m
?
su
p
85 port
cm
48 cm
table top (?)
3.
35 mm
5·7 m
1.
A hinged table top is supported by a
metal bracket.
Calculate the width of the table top.
4.
ΔABC is isosceles with AC = BC = 140 mm.
AB = 110 mm.
A
110 mm
Calculate the height of the triangle.
(shown as a dotted line).
B
140 mm
? cm
5.
C
6·5 cm
5·7 cm
An eraser has a wedge shaped edge.
Calculate the length of the sloping edge.
1·5 cm
this is Chapter Thirteen
page 76
©TeeJay Publishers
General Homework for Book 3G
Ch 13 - Pythagoras
Exercise 7E
y
(a) Write down the coordinates
of the points L and M ?
8
7
6
5
4
3
2
1
(b) COPY the figure accurately
showing the 2 points.
(c) Join L to M and make a right
angled triangle.
(d) Use Pythagoras Theorem to calculate
the length of the line LM.
y
2.
•
8
7
6
5
4
3
2
1
S
1 2 3 4 5 6 7 8 9 10
3.
•M
•L
1 2 3 4 5 6 7 8
(b) Copy the figure accurately
showing the 2 points, S and T.
(c) Join S to T, complete the
right angled triangle and calculate
the length of the line ST.
x
(a) Draw your own coordinate diagram measuring 8 boxes across
by 8 boxes upwards.
(b) Mark on it the x-axis, the y-axis and the origin.
(c) Plot the 2 points, J(1,3) and K(7,7).
(d) Create a right angled triangle and calculate the length of the line JK.
Exercise 8E
1.
Decide whether to use c 2 = a 2 + b2 or a 2 = c 2 – b2 in each of these :–
(a)
(b)
mm
5
2
m
zc
13 mm
w mm
this is Chapter Thirteen
x
(a) Write down the coordinates
of the points S and T.
PY
O
C
•T
CO
PY
1.
11 cm
page 77
8 cm
©TeeJay Publishers
2.
General Homework for Book 3G
Ch 13 - Pythagoras
One of the following two answers is known
to be the correct value for x.
x = 19·5 cm or x = 16·4 cm
x cm
Without actually doing the calculation, say
which one it must be and why the other is
obviously wrong.
18 cm
7·5 cm
3.
Calculate the length of the
missing side in this plastic
set square.
20
cm
? cm
helix
11·5 cm
4.
5·
5
ft
8·
5
This metal frame, in the shape
of a right angled triangle, is
placed on the ground ready for
a tent canvas to be spread over it.
ft
Calculate the distance, along the
ground, between the ends of the
2 metal poles.
ground
? ft
5.
A bird table top is supported
by two sloping strips of wood.
ΔAPB is isosceles.
Calculate the length of the
table top (AB). Careful !!
this is Chapter Thirteen
table top
A
B
41
·2
cm
30 cm
P
page 78