Question

the length of a rectangle is five times its width. if the area of the rectangle is 180 yd², find its perimeter.

Explanation:

Step1: Define variables for width

Let width = $w$

Step2: Define length in terms of $w$

Length = $5w$

Step3: Set up area equation

Area: $w \times 5w = 180$
$5w^2 = 180$

Step4: Solve for $w^2$

$w^2 = \frac{180}{5} = 36$

Step5: Solve for $w$

$w = \sqrt{36} = 6$ yd

Step6: Find length

Length = $5 \times 6 = 30$ yd

Step7: Calculate perimeter

Perimeter = $2(w + \text{length}) = 2(6 + 30)$
$= 2 \times 36 = 72$ yd

Answer:

72 yd