What is the perimeter of the walkway around the pool?

• A. 130 feet
• B. 170 feet
• C. 110 feet
• D. 150 feet

Answer: (D)

Perimeter around a pool with a uniform walkway is found by treating the pool plus the walkway as one bigger rectangle. If the pool has length L and width W, and the walkway around it has width w, then the outer rectangle has dimensions (L + 2w) by (W + 2w). The distance around that outer edge is P = 2[(L + 2w) + (W + 2w)] = 2L + 2W + 8w. This shows how adding a walkway increases the perimeter: you add 8 times the walkway width to the pool’s own perimeter.

In this problem, plugging the pool’s dimensions and the walkway width from the diagram into P = 2L + 2W + 8w gives 150 feet. For example, if the pool is 20 by 15 feet and the walkway is 10 feet wide, the outer perimeter is 2(20 + 15) + 8(10) = 70 + 80 = 150 feet.