Question

the length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 54 yd, find its length and width. length: □ yd width: □ yd

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) yd. Then the length \( l=(w + 3) \) yd.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P = 2(l + w) \). Given \( P=54 \) yd. Substitute \( l=(w + 3) \) into the formula: \( 54=2((w + 3)+w) \).
Simplify the equation:

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Step3: Solve for \( w \)

Subtract 6 from both sides: \( 54 - 6=4w \), so \( 48 = 4w \). Then \( w=\frac{48}{4}=12 \) yd.

Step4: Solve for \( l \)

Since \( l=w + 3 \), substitute \( w = 12 \): \( l=12+3 = 15 \) yd.

Answer:

length: \( 15 \) yd, width: \( 12 \) yd