Word Problem

Question

A rectangular garden measures 16 feet by 12 feet. A path of uniform width is to be added so as to surround the entire garden. The landscape designer doing the work the garden wants the garden and path to cover an area of 320 square feet. How wide should the path be? 

Answer 1

Let x=width of the garden, then the length and width of the garden/path would be 16+2x and 12+2x.

 

Area = l x w

 

320 = (16+2x)(12+2x)  and solve for x

 

320 = 4x² + 56x + 192

 

80 = x² + 14x + 48

 

x² + 14x - 32 = 0

 

(x+16)(x-2) = 0,  x is either -16 (which is impossible) or x=2