A 16 ft by 18 ft rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 440 $\mathrm { ft } ^ { 2 }$ ?
A) 2 ft
B) 3.5 ft
C) 1 ft
D) 3 ft

Question

Quizplus · Accepted Answer

The width of the path can be found by setting up an equation based on the area. The area of the garden is 16 ft * 18 ft = 288 ft^2. If the total area including the path is 440 ft^2, then the area of the path alone is 440 ft^2 - 288 ft^2 = 152 ft^2. Let x be the width of the path. The overall dimensions of the garden plus the path are (16 + 2x) by (18 + 2x). The equation for the total area is then (16 + 2x)(18 + 2x) = 440. Simplifying this equation will eventually lead to finding that x = 2, meaning the path is 2 ft wide.

A 16 Ft by 18 Ft Rectangular Garden Is to Have