Number And Algebra - Chapter 7 Applying Ratios And Rates - Nelson Think Math Page 24
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32N E L S O N T H I N K M A T H S
8
A u s t r a l i a n C u r r i c u l u m
for the
Solution
a
Write the scale.
1 : 5000
Write the scale for 5 cm on the map.
5 cm : 25 000 cm
Convert the real measurement to metres.
25 000 cm ¼ 250 m
b
Measure the map distance.
Map distance ¼ 10.8 cm
Multiply by 5000.
Real distance ¼ 54 000 cm
Convert to metres.
¼ 540 m
You can use the scale of similar drawings to find unknown sides, just as you use the scale of a scale
drawing or map.
Example
19
The quadrilaterals shown below are similar.
F
B
E
A
5 cm
6 cm
C
9 cm
G
D
8.1 cm
H
a
Find the scale that relates ABCD to EFGH.
b
Find the length of FG.
c
Find the length of CD.
Solution
a
Identify known corresponding sides.
EH corresponds to AD.
EH
Use them to find the scale factor.
Scale factor ¼
AD
9
3
¼
¼ 1:5 or
6
2
Write the answer.
The scale factor is 1.5. EFGH is an
enlargement of ABCD by 1.5 times.
b
Identify the side corresponding to FG.
FG corresponds to BC.
Relate using the scale factor.
FG ¼ 1:5 3 BC
¼ 1:5 3 5 cm
¼ 7:5 cm
c
Identify the side corresponding to CD.
CD corresponds to GH.
Relate using the scale factor.
GH ¼ 1.5 3 CD
GH
Divide by 1.5 to find CD.
CD ¼
1:5
8:1
Substitute the value of GH.
¼
1:5
Calculate the answer.
¼ 5.4 cm
261
9780170214148
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