PSAT Math Multiple-Choice Question 642: Answer and Explanation

Question: 642

On a map of a rectangular fenced-in area, the drawing of the enclosed area has a surface area of 20 square inches. If one side of the fenced-in area drawing is 4 inches long and the key of the map indicates that for every 1 inch drawn on the map there are 6 feet in actual distance, what is the perimeter of the actual fence, assuming there are no gaps or gates?

• A. 18 ft
• B. 108 ft
• C. 120 ft
• D. 720 ft

Correct Answer: B

Explanation:

(B) The area of a rectangle is given by the formula A = lw, where l is length and w is width. If the length of the drawing is 4 inches, we know from dividing both sides of our area equation by the length that:

The key tells us that each inch on the map represents 6 feet. We can multiply 4 inches by 6 feet/inch to tell us that the length is 24 feet. Similarly, we can multiply the 5-inch width by 6 feet/inch to tell us that the width is 30 feet.

Alternatively, you could have solved for actual distance by setting up a proportion. For the length, the proportion might look something like:

Cross multiplying gives you:

1x = (4)(6)

So x = 24.

The question wants to know the perimeter of the fence. Perimeter of a rectangle is given by the formula P = 2l + 2w. Plugging our dimensions into the formula tells us:

P = 2(24) + 2(30) = 48 + 60 = 108

The correct answer is choice (B).