A rectangular garden has dimensions of 18 feet by 15 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 234 square feet?
A) 5.5 feet
B) 5 feet
C) 4 feet
D) 3 feet

Question

Quizplus · Accepted Answer

The area of the garden is 18 feet * 15 feet = 270 square feet. The total area, including the path, minus the garden area equals the area available for the path, which is 234 square feet. Let the width of the path be x feet. The dimensions of the garden plus the path will be (18 + 2x) by (15 + 2x). The equation for the area of the path is: (18 + 2x)(15 + 2x) - 270 = 234. Simplifying this equation to find x is complex, so instead, we can test the options given:For D) 3 feet: The dimensions including the path would be 24 feet by 21 feet. The total area would be 24 * 21 = 504 square feet. Subtracting the garden's area (270 square feet) gives us 234 square feet for the path, which matches the gravel available. Therefore, the path can be 3 feet wide.

A Rectangular Garden Has Dimensions of 18 Feet by 15