A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?

Question

Quizplus · Accepted Answer

The area of the garden is 12 * 5 = 60 square feet. The total area, including the path, is 60 + 138 = 198 square feet. Let the width of the path be x feet. The dimensions of the garden plus the path are (12 + 2x) by (5 + 2x). The equation for the total area is (12 + 2x)(5 + 2x) = 198. Simplifying, we get 4x^2 + 34x + 60 = 198, which simplifies to 4x^2 + 34x - 138 = 0. Solving for x, we find that x = 3 feet is the width of the path that allows for 138 square feet of gravel.

A Rectangular Garden Is 12 Feet by 5 Feet