Question

Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy

A
10 m
B
F
E
8 m
D
D
С
G
Design
Photocopy
The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image? (5 points)

Answer 1

12 m

Explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

`(AD)/(EH) = (2)/(3)`

`(8)/(EH) = (2)/(3)`

Cross multiply

`3*8 = 2*EH`

`24 = 2*EH`

Divide both sides by 2 to make EH the subject of formula

`(24)/(2) = (2*EH)/(2)`

`12 = EH`

The length of side EH = 12 m