Question

Find the lengths of the missing sides on the similar shapes at right.

Answer 1

Given the following two similar figures and it the pair of corresponding sides:

54 mm : y

15 mm : z

22 mm : 33 mm

x : 40 mm

Let's determine the measure of the missing sides using ratios and proportion:

For y,

`\text{ 54 mm : y = 22 mm : 33 mm}`
`\text{ }\frac{\text{ 54 mm}}{\text{ y}}\text{ = }\frac{\text{ 22 mm}}{\text{ 33 mm}}`
`\text{ (54 mm)(33 mm) = (22 mm)(y)}`
`\text{ }\frac{\text{(54 (mm))(33 mm)}}{\text{ 22 (mm)}}\text{ = y}`
`\text{ }\frac{\text{ 54 x 33}}{\text{ 22}}\text{ mm = y}`