Let X be the width of the path.
The width of the path would be the width of the pool plus 2x, so 2x +16
The length of the path would be the length of the pool plus 2x, so 2x+22
The total area is 832 square feet.
Area is found by multiplying the length by the width.
So you have:
(2x+16) (2x+22) = 832
Use the Foil Method:
(2x+16) (2x+22) = 4x^2 +76x+352
Now you have:
4x^2 +76x+352 = 832
Subtract 832 from both sides:
4x^2 +76x+352-832 = 0
Simplify:
4x^2 +76x -480
Factor the left side:
4(x-5)(x+24) = 0
Divide both sides by 4:
(x-5)(x+24) = 0
Set both parenthesis to equal 0 and solve for x:
x=5 and x = -24
The width of the path cannot be a negative number, so the width is 5 meters.
