Question

1. the perimeter of a rectangle is 80 feet. if the area is 336 square feet, and each side is a whole number of feet in length, what are the lengths of this rectangle’s sides?

Explanation:

Step1: Recall rectangle formulas

Let length be \( l \), width be \( w \). Perimeter \( P = 2(l + w)=80 \), so \( l + w = 40 \). Area \( A = lw = 336 \).

Step2: Express \( l = 40 - w \), substitute into area

\( (40 - w)w = 336 \) → \( 40w - w^2 = 336 \) → \( w^2 - 40w + 336 = 0 \).

Step3: Solve quadratic equation

Factor: \( (w - 12)(w - 28)=0 \). So \( w = 12 \) or \( w = 28 \). Then \( l = 28 \) or \( l = 12 \).

Answer:

The side lengths are 12 feet and 28 feet.