The area of the rectangle is 576 square inches.
Work Step by Step
To find the area of the rectangle, we need to know both the length and the width of the rectangle. To find the width, we use the perimeter equation. The formula for the perimeter of the rectangle is width + width + length + length. Let w represent the width and l represent the length. Recall: Perimeter = 2w + 2l Since the perimeter is 100 inches and the length is 32 inches, we can write the equation as: 100 = 2w + 2$\times$ 32 100 = 2w + 64 36 = 2w Divide both sides by 2. w = 18 Now that we know both width and length, we can find the area. Area of a rectangle is equal to width $\times$ length. Area = w $\times$ l Area = 18 $\times$ 32 Area = 576 The area of the rectangle is 576 square inches.