Question

The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway? Use the picture below to help you.

Answer 1

(2x+7)(2x+9) = 143

Answer 2

So the sides of the bigger rectangle are 7+x+x and 9+x+x
The area is just side*other side
so (7+2x)(9+2x)=143
63+4x^2+32x=143
4x^2+32x-80=0
x^2+8x-20=0
(x+10)(x-2)=0
x=2 or x=-10 (-10 is silly in this case so the only solution is x=2)

Answer 3

4x^2 + 14x + 18x + 63 = 143
4x^2 + 32x - 80 = 0
x^2 +8x -20=0
x^2 + 10x - 2x - 20 = 0
(x+10)(x-2) = 0
x = 2 since -10 cant be