SOLUTION: An open rectangular gutter is made by turning up the sides 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.

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Question 109246This question is from textbook Introductory Algebra
: An open rectangular gutter is made by turning up the sides 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 ankor@dixie-net.com(22740) About Me  (Show Source):
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An open rectangular gutter is made by turning up the sides 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.
:
Let x = depth of gutter
:
The cross section would look sort of like this:
x|__|x
:
The bottom = (20 - 2x)
:
Area:
x(20-2x)= 50
-2x^2 + 20x - 50 = 0
Divide equation by -2 to simplify
x^2 - 10x + 25 = 0
Factors to:
(x-5)(x-5) = 0
x = 5 inches is depth of the gutter
:
:
Check:
Bottom = 20 - 2(5) = 10
5 * 10 = 50 sq/in as given