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

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

Step2: Find patio width (similar rectangles)

Set up proportion: $\frac{\text{Patio length}}{\text{Backyard length}} = \frac{\text{Patio width}}{\text{Backyard width}}$
$\frac{18}{45} = \frac{w_{patio}}{20} \implies w_{patio} = 20 \times \frac{18}{45} = 8$

Step3: Calculate patio perimeter

Use rectangle perimeter formula: $P = 2(l + w)$
$P_{patio} = 2(18 + 8) = 2(26) = 52$

Answer:

Backyard perimeter: 130 feet
Patio perimeter: 52 feet