SOLUTION: You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What is t

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What is t      Log On


   

Question 925988: You have a pool that measure 15 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 250 square yards. What is the width of the deck?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, the uniform width around the pool.

%2815%2B2x%29%2810%2B2x%29-15%2A10=250; you want the difference in area to be 250 square yards. Simplify this equation.

%2815%2B2x%29%2810%2B2x%29=250%2B150
15%2A10%2B50x%2B4x%5E2=250%2B150
50x%2B4x%5E2=250
25x%2B2x%5E2=125
2x%5E2%2B25x-125=0

You can try to factor, but alternatively, preparing for general solution method,
discriminant is 25%5E2-4%2A2%28-125%29=625%2B8%2A125=1625=25%2A65=5%2A5%2A5%2A13.

x=%28-25%2Bsqrt%285%5E3%2A13%29%29%2F4

highlight%28x=%28-25%2B5%2Asqrt%2865%29%29%2F4%29
About 3.83 yards.
About 3 yards 2 feet 6 inches