Ratios, Scale Factors and Similar Triangles 2
Y9
Diagrams not to scale
1).
Triangle T enlarges on to Triangle U.
Find
a).
the length scale factor,
b).
the area scale factor,
c).
the value of x.
T
x cm
y cm
5 cm
6).
Triangles J and K are similar triangles.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle J
if Triangle K is 15.1875 cm2.
7).
Triangles C and D are similar triangles.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle D
if Triangle C is 6 cm2.
M
x cm
L
7 cm
3).
Triangle T enlarges on to Triangle U.
Find
a).
the length scale factor,
b).
the value of x,
c).
the value of y,
d).
the area of Triangle U
if Triangle T is 6 cm2.
5).
Triangle A enlarges on to Triangle B.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle A
if Triangle B is 13.5 cm2.
U
4.2 cm
2).
An enlargement of length scale factor 3, maps
Triangle L on to Triangle M.
Find
a).
the length x,
b).
the length y,
c).
the area scale factor,
d).
the area of M if the area
of Triangle L is 12 cm2.
4).
Triangle F enlarges on to Triangle G.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle F
if Triangle G is 54 cm2.
12 cm
6 cm
y cm
T
3 cm
20
4 cm
cm
12 cm
U
x cm
3 cm
3.4 cm
1.5 cm
F
y cm
9 cm
x cm
G
42 cm
4 cm
A
y cm
x cm
6 cm
B
3 cm
9 cm
4 cm
2 cm
y cm
C
J
y cm
2 cm
x cm
K
11.25 cm
7.875 cm
D
6 cm
2.5 cm
x cm
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8).
Triangles E and F are similar triangles.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle F if Triangle E is 54 cm2.
9).
Triangles G and H are similar triangles.
Find
a).
the value of x,
b).
the value of y,
c).
the area of Triangle H if Triangle G is 87.5 cm2.
10).
Triangles P and Q are similar. The area of
P is 30 cm2 and the area of Q is 120 cm2.
Find
a).
the value of x,
b).
the value of y,
c).
the value of z.
11).
Triangles S and T are similar. The area of
S is 5.5 cm2 and the area of P is 88 cm2.
Find
a).
the value of x,
b).
the value of y,
c).
the value of z.
Y9
9cm
x cm
y cm
x cm
3 cm
E
18 cm
15 cm
F
5 cm
H
3 cm
y cm
22.5 cm
P
y cm
2.5 cm
G
26 cm
12 cm
Q
z cm
x cm
x cm
4 cm S
y cm
12). In the triangle UXY, VW is parallel to XY.
VW = 16 cm and XY = 24 cm.
a).
Prove that triangles UXY and UVW are similar.
b).
If UV = 12 cm, find the distance UX.
c).
If UY = 9 cm, find the distance UW.
d).
The area of triangle UVW = 40 cm2,
find the area of the triangle UXY.
4 cm
14 cm
z cm
T
22 cm
U
V
X
16 cm
24 cm
13). In the triangle ABC, ED is parallel to CB. ED = 8 cm and CB = 20 cm.
a).
Prove that triangles ABC and ADE are similar.
b).
If AE = 4 cm, find the distance
A
i).
AC,
ii)
EC.
D
E
c).
If AB = 15 cm, find the distance
8 cm
i).
AD,
ii).
DB.
C
20 cm
d).
The area of triangle AED = 7 cm2,
find the area of the trapezium EDCB.
W
Y
B
14). In triangle XYZ, XV = 4 cm, XZ = 16 cm, XW = 5 cm, WY = 15 cm and ZY = 24 cm.
Do not assume that VW and ZY are parallel.
a).
Prove that triangles XYZ and XWY are similar.
b).
Find the length of VW.
X
c).
If triangle XYZ = 120 cm2,
W
find the area of
V
i).
triangle XVW,
Z
Y
24 cm
ii).
trapezium VWYZ.
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Similar Shapes
Y9
The following table shows the measurements of the base and area of two similar shapes.
Copy and complete the table.
Linear
Scale Factor
1).
2).
3).
4).
5).
6).
7).
8).
9).
10).
11).
12).
13).
14).
15).
16).
17).
18).
19).
20).
21).
22).
23).
24).
25).
26).
27).
28).
29).
30).
31).
32).
33).
34).
35).
36).
37).
38).
39).
40).
41).
42).
43).
44).
45).
46).
47).
48).
3
2
5
4
1.5
3.5
2 1/4
3
/4
Smaller Shape 1
Base (m)
Area (m2)
4
8
4
Larger Shape 2
Base (m)
Area (m2)
12
3
18
3
15
40
1 1/3
3
7
6
7
2.6
8.1
8.3
3.5
4.3
8.8
4.6
10.4
12.5
4.7
18.4
3.9
2.3
5.7
14
81
15
12
8
14
34
18
12
26.4
12
21
36
42
7.8
16.2
58.1
17.5
25.8
20.24
23.46
15.6
67.5
50.29
79.12
24.18
8.7
4
4.6
6.7
5.7
343
225
49.5
139.968
80.143
326.74
160
2.8
23.2
7.2
6 2/3
11.4
72
144
8
4 1/2
4.5
20
40
18
42
72
34.8
30
5
6.3
Area
Scale Factor
12
20
13
12
7
14
15
5
12.5
6.9
5.6
4.3
5.9
8.2
7.3
24
21
72
84
22.54
7.56
33.5
49.02
18.62
475.2
96.75
17
/12
32
48
320
208
108
567
896
60
980
162
66.309
29.624
75.852
153.459
4
25
16
9
36
2.25
1
/4
1 7/9
295.84
26.353
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