Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 90 in, find its length and width. length: in width: in

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) inches. Then the length \( l = 4w \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 4w \) and \( P = 90 \) into the formula:

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Step3: Solve for \( w \)

Divide both sides of the equation \( 90 = 10w \) by \( 10 \):

$$ w=\frac{90}{10}=9 $$

Step4: Solve for \( l \)

Since \( l = 4w \), substitute \( w = 9 \) into the equation:

$$ l=4\times9 = 36 $$

Answer:

length: \( 36 \) in, width: \( 9 \) in