Question

modeling real life your family decides 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 perimeter of your backyard and the perimeter of the patio.

backyard perimeter: feet
patio perimeter: feet

Explanation:

Step1: Calculate backyard perimeter

Perimeter formula: $P = 2(l + w)$
$P_{backyard} = 2(45 + 20)$
$P_{backyard} = 2(65) = 130$

Step2: Find similarity ratio

Ratio of patio to backyard length: $\frac{18}{45} = \frac{2}{5}$

Step3: Calculate patio width

Use similarity ratio: $w_{patio} = 20 \times \frac{2}{5} = 8$

Step4: Calculate patio perimeter

$P_{patio} = 2(18 + 8)$
$P_{patio} = 2(26) = 52$

Answer:

Backyard perimeter: 130 feet
Patio perimeter: 52 feet