Question

the perimeter of a rectangle is 148 feet. its two longest sides add up to 86 feet. what is the length of each of its two shortest sides? a. 31 feet b. 42 feet c. 62 feet d. 72 feet

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2l + 2w \), where \( l \) is the length (longer side) and \( w \) is the width (shorter side).

Step2: Substitute known values

We know \( P = 148 \) feet and the sum of the two longest sides (2l) is 86 feet. Substitute into the formula: \( 148 = 86 + 2w \).

Step3: Solve for \( w \)

Subtract 86 from both sides: \( 2w = 148 - 86 = 62 \). Then divide by 2: \( w = \frac{62}{2} = 31 \).

Answer:

a. 31 feet