Write the word or phrase that best completes each statement or answers the question.
-The perimeter of a rectangle is 40 inches and its area is 96 square inches. What are its dimensions?
A)8 in. by 12 in.
B)7 in. by 13 in.
C)9 in. by 11 in.
D)7 in. by 11 in.

Question

Quizplus · Accepted Answer

Let the length be L and the width be W. The perimeter is 2L + 2W = 40, or L + W = 20. The area is LW = 96. We can use substitution to solve for L or W. For example, W = 20 - L, so we have L(20 - L) = 96, or 20L - L^2 = 96. Rearranging, we get L^2 - 20L + 96 = 0. Factoring, we get (L - 8)(L - 12) = 0, so L = 8 or L = 12. If L = 8, then W = 12, and if L = 12, then W = 8. Either way, we get a rectangle with dimensions of 8 inches by 12 inches. Therefore, the answer is A.

Write the Word or Phrase That Best Completes Each Statement