SOLUTION: A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be?

Question 269238: A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be?
Let x be the uniform width of the walk. Then the length and width of the rectangle bounded by the outer edge of the walk are 40+2x and 20+2x respectively. The area of the walk is the total area of the outer rectangle minus the area of the pool or:
(20+2x)*(40+2x) - 20*40 = 700
40*20 + 40x + 80x + 4x^2 - 800 = 700
800 +120x + 4x^2 - 800 = 700
4x^2 + 120x - 700 = 0
Divide both sides by 4:
x^2 + 30x - 175 = 0
Factor the above:
(x+35)*(x-5) = 0
The solution for x must satisfy either x+35 = 0 and/or x-5 = 0
These solutions are x = -35 and x = 5. Since the width must be positive, the correct value for x must be 5.
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