Question

the length of a rectangle is 4 ft longer than its width. if the perimeter of the rectangle is 52 ft, find its length and width. length: ft width: ft

Explanation:

Step1: Let the width be \( x \)

Let the width of the rectangle be \( x \) ft. Then the length is \( (x + 4) \) ft.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \( P=2(l + w) \). Given \( P = 52 \) ft.
Substitute \( l=x + 4 \) and \( w=x \) into the formula: \( 52=2((x + 4)+x) \).
Simplify the equation:

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Step3: Solve for \( x \)

Subtract 8 from both sides: \( 52-8=4x \), so \( 44 = 4x \).
Divide both sides by 4: \( x=\frac{44}{4}=11 \).

Step4: Find the length

Since the length \( l=x + 4 \), substitute \( x = 11 \). Then \( l=11 + 4=15 \).

Answer:

length: \( 15 \) ft
width: \( 11 \) ft