Question

the length of a rectangle is 5 in longer than its width. if the perimeter of the rectangle is 66 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 \( l=w + 5 \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P = 2(l + w) \). Given \( P=66 \) inches. Substitute \( l=w + 5 \) into the formula:

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Step3: Solve for \( w \)

Subtract 10 from both sides: \( 66-10 = 4w\), so \( 56=4w \). Divide both sides by 4: \( w=\frac{56}{4}=14 \) inches.

Step4: Solve for \( l \)

Since \( l=w + 5 \), substitute \( w = 14 \): \( l=14 + 5=19 \) inches.

Answer:

length: \( 19 \) in, width: \( 14 \) in