SOLUTION: An above-ground swimming pool with a square base is to be constructed such that the surface area of the pool is 465 square feet. The height h of the pool is to be 4 feet (see figur

Algebra ->  College  -> Linear Algebra -> SOLUTION: An above-ground swimming pool with a square base is to be constructed such that the surface area of the pool is 465 square feet. The height h of the pool is to be 4 feet (see figur      Log On


   

Question 994448: An above-ground swimming pool with a square base is to be constructed such that the surface area of the pool is 465 square feet. The height h of the pool is to be 4 feet (see figure.) What should the dimensions of the base be? (Hint: The surface area is S = x2 + 4xh.)
length ft
width ft

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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The base is square so length and width are the same.
L=W=x; h=height=4ft
Surface area=area of bottom+area of sides
SA=x%5E2%2B4xh
SA=x%5E2%2B16x
465ft%5E2=x%5E2%2B16x
0=x%5E2%2B16x-465
0=%28x-15%29%28x%2B31%29%0D%0A%7B%7B%7Bx-15=0 OR x%2B31=0
x=15 OR x=-31
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Since -31 does not work,
x=15 feet
ANSWER: The length and the width are 15.
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CHECK:
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SA=x%5E2%2B4xh
465ft%5E2=%2815ft%29%5E2%2B4%2815ft%29%284ft%29
465ft%5E2=225ft%5E2%2B240ft%5E2
465ft%5E2=465ft%5E2