Question

the length of a rectangle is 3 ft longer than its width. if the perimeter of the rectangle is 50 ft, find its length and width. length: ft width: ft

Explanation:

Step1: Set up variables

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

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P = 2(l + w) \). Given \( P = 50 \) ft, substitute \( l=(w + 3) \) into the formula:

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Step3: Solve for \( w \)

Subtract 6 from both sides: \( 50-6=4w \), so \( 44 = 4w \). Then divide both sides by 4: \( w=\frac{44}{4}=11 \) ft.

Step4: Solve for \( l \)

Since \( l=w + 3 \), substitute \( w = 11 \): \( l=11 + 3=14 \) ft.

Answer:

length: \( 14 \) ft, width: \( 11 \) ft