Digital PSAT Math Practice Question 297: Answer and Explanation

Question: 297

A rectangular fence, which fully encloses a flat area, is 4 times as long as it is wide. If the length of the fence is L feet, what is the perimeter of the fence in terms of L?

• A. 2.5L
• B. 10L
• C. 16L
• D. 16L²

Correct Answer: A

Explanation:

(A) Let L denote the length and W denote the width of the rectangular fence. You are told that the fence is 4 times as long as it is wide. In other words, L = 4W. Now, the formula for the perimeter of a rectangle is P = 2L + 2W. The problem asks for the perimeter in terms of L, so you need to replace the W in the perimeter equation with an expression involving L. Since L = 4W, you can solve for W by dividing both sides by 4 to obtain . Plugging this expression in for W in your perimeter equation gives P = 2L + 2W = 2L + 2(0.25L) = 2L + 0.5L= 2.5L, which is choice (A).