A rectangular garden is 20 feet long and 10 feet wide. A path of uniform width is built around the garden. If the area of the path is equal to the area of the garden, what is the width of the path?
Correct: A
Area of the garden = 20 * 10 = 200 sq ft. Let the width of the path be 'w'. The new dimensions of the garden including the path are (20 + 2w) and (10 + 2w). The area of the garden and path is (20 + 2w)(10 + 2w). The area of the path is (20 + 2w)(10 + 2w) - 200. Given that the area of the path is equal to the area of the garden, we have (20 + 2w)(10 + 2w) - 200 = 200 => (20 + 2w)(10 + 2w) = 400 => 200 + 60w + 4w^2 = 400 => 4w^2 + 60w - 200 = 0 => w^2 + 15w - 50 = 0 => (w + 20)(w - 2.5) = 0. Since width cannot be negative, w = 2.5 feet.