PSAT Math Multiple-Choice Question 161: Answer and Explanation

Question: 161

Equal amounts of fencing are used to surround both an octagonal area and a square area. If each side of the octagon is 5 yards shorter than each side of the square, how many yards of fencing are needed to surround each area?

• A. 20
• B. 40
• C. 60
• D. 80

Correct Answer: B

Explanation:

B

The question asks how many yards of fencing are needed to surround each area. There are numbers in the answer choices, so plug in the answers. Start with one of the middle choices. Try (B). If 40 yards of fencing are needed for each area, then the perimeter of each area is 40 yards. Begin with the square area. If the perimeter of a square area is 40 yards, then each side is 40 ÷ 4 = 10 yards. The side of the octagon is 5 yards shorter than this, which is 10 - 5 = 5. The perimeter of the octagon must match the perimeter of the square, so find the perimeter of the octagon, which is 8 × 5 = 40. Since this is equal to the perimeter of the square area, the correct answer is (B).