Question

MODELING WITH MATHEMATICS Your family has decided to put a rectangular patio in your backyard, similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeters of your backyard and of the patio.

Backyard perimeter $=$

ft


Patio perimeter $=$

ft

Answer 1

Back yard: 130 feet.

The patio: 56 feet

Explanation:

Perimeter of the back yard:

45 + 45 + 20 + 20 = 130 feet

Perimeter of the patio:

We have the width we need the length of the patio. Since they are similar we can set up a proportion

`(18)/(45)` =
`(x)/(20)` We can simplify
`(18)/(45)` to
`(2)/(5)` by dividing the top and bottom by 9.

`(2)/(5)` =
`(x)/(20)`

5 x 4 = 20

2 x 4 = 8

x = 8.

8 +8 + 20 + 20 = 56