A shed that measures 8 feet by 11 feet has a brick pathway of constant width built around it, so that the outer edge of the pathway is also a rectangle. The total area of the pathway is 120 square feet. What is its width (in feet)?

Logic Jul 23, 2019

#1**+2 **

The pathway will consist of 4 squares each with a side of x, two rectangles with dimensions of 8 *x and two rectangles with dimensions of 11*x ...... where x is the width of the path

4x^2 + 2(8*x) + 2(11*x) = 120

4x^2 + 16x + 22x = 120

4x^2 + 38x = 120

4x^2 + 38x - 120 = 0 factor

(x + 12)(4x - 10)= 0 set each factor to 0 ans solve for x

x + 12 = 0 4x - 10 = 0

x = -12 (reject) 4x = 10

x = 10/4 = 5/2 = 2.5 ft

So.....the path width is 2.5 ft

CPhill Jul 23, 2019