Question

Polygon A is similar to Polygon B.

Find the perimeter of Polygon B.
24
A
PA = 128
15
B
PB = [?]

Answer 1

`P_(B)` = 80

Explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

`(ratioA)/(P_(A) )` =
`(ratioB)/(P_(B) )` , that is

`(8)/(128)` =
`(5)/(P_(B) )` ( cross- multiply )

8
`P_(B)` = 5 × 128 = 640 ( divide both sides by 8 )

`P_(B)` = 80