SOLUTION: A rain gutter is to be made of aluminum sheets that are 36 inches wide by turning up the edges 90degrees. What depths will allow at least 90 square inches of water to​ flow?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A rain gutter is to be made of aluminum sheets that are 36 inches wide by turning up the edges 90degrees. What depths will allow at least 90 square inches of water to​ flow?      Log On


   

Question 1153350: A rain gutter is to be made of aluminum sheets that are 36 inches wide by turning up the edges 90degrees. What depths will allow at least 90 square inches of water to​ flow?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the depth of the gutter; then the width of the gutter is (36-2x).

We need the cross sectional area to be greater than or equal to 90:

x%2836-2x%29+%3E=+90
36x-2x%5E2+%3E=+90
2x%5E2-36x%2B90+%3C=+0
x%5E2-18x%2B45+%3C=+0
%28x-15%29%28x-3%29+%3C=+0

The product is negative for any value of x between 3 and 15.

ANSWER: A cross sectional area of at least 90 square inches will be obtained for any depth between 3 and 15 inches.