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

IneedHALP Mar 12, 2019

#2**+2 **

The area f the shed = 8 * 11 = 88 ft^2

The area of the path is 120ft^2

So...the combined area is 208 ft^2

Let the width of the path = x

And we have this equation

(shed width + 2*path width) (shed length + 2*path width) = 208

(8 + 2x) ( 11 + 2x) = 208 simplify

88 + 22x + 16x + 4x^2 = 208

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

(2x - 5) (2x + 24) = 0

Only the first factor will give a positive answer

2x - 5 = 0

2x = 5

x = 5/2 = 2.5 ft = path width

CPhill Mar 12, 2019