The perimeter of a rectangle is 30 inches and its area is 54 square inches. Find the length and width of the rectangle.
A) 5 in. by 8 in.
B) 8 in. by 9 in.
C) 9 in. by 10 in.
D) 6 in. by 9 in.
E) 6 in. by 11 in.

Question

Quizplus · Accepted Answer

Let L be the length and W be the width. We have the perimeter equation: 2L + 2W = 30 (simplifies to L + W = 15). We also have the area equation: LW = 54. We can use substitution to solve for L or W in terms of the other variable. For example, we can solve for L: L = 15 - W. Substituting this into the area equation, we get W(15 - W) = 54. Simplifying and rearranging, we get W^2 - 15W + 54 = 0. This factors to (W - 6)(W - 9) = 0, so W = 6 or W = 9. If W = 6, then L = 15 - 6 = 9. If W = 9, then L = 15 - 9 = 6. Therefore, the possible dimensions are 6 inches by 9 inches or 9 inches by 6 inches. However, since length and width are interchangeable in a rectangle, both of these dimensions represent the same rectangle. Therefore, the best choice is D.

The Perimeter of a Rectangle Is 30 Inches and Its