SOLUTION: I am not sure how to do this problem. I appreciate all the help I can get. Problem: An open retangular gutter is made by turning up the side of a piece of metal 20 in. wide. Th

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Question 126667This question is from textbook Introductory Algebra
: I am not sure how to do this problem. I appreciate all the help I can get. Problem: An open retangular gutter is made by turning up the side of a piece of metal 20 in. wide. The area of the cross section of the gutter is 50 in.^2. Find the depth of the gutter.
 This question is from textbook Introductory Algebra

Answer by solver91311(24713) About Me  (Show Source):
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To make a gutter, you have to fold up two sides. Since it is a rectangle, you have to fold up the same amount on both sides. We'll call this x, because that is the measure of the depth that we want to know to answer the problem anyway.

Since x is the amount folded up on one side, 2x is the amount folded up altogether. The bottom of the gutter is then the original 20 inches minus the 2x inches folded up.

The cross-section area of the gutter, given as 50cm%5E2 is calculated by the length of the rectangle times the width, or x%2820-2x%29

So we can say: x%2820-2x%29=50

20x-2x%5E2=50
-2x%5E2%2B20x-50=0
x%5E2-10x%2B25=0
%28x-5%29%28x-5%29=0

x=5

So the depth of the gutter is 5 inches.

Check.
If the depth is 5, then 5 inches were folded up on each side making 10 inches. The original 20 inches - 10 inches is 10 inches. 10 X 5 = 50. Answer checks.