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a rain gutter is made from sheets of aluminum that are 27 inches wide.
The edges are turned up to form right angles.
Determine the depth of the gutter that will allow a cross-sectional area of 58 inches.
There are 2 solutions to this problem.
end view y=depth, x=width:
2y + x = 27"
x = (27-2y)
Cross sectional area
x*y = 58 sq/inches
Replace x with (27-2y)
y(27-2y) = 58
-2y^2 + 27y - 58 = 0
Use the quadratic formula to find y
In this equation x=y; a=-2; b=27; c=-58
y = +10.82 inches is the depth
y = +2.68 inches is the depth
Both these solutions satisfy the requirement, the width will vary accordingly
Check solution using the last solution
2(2.68) + x = 27
x = 27 - 5.36
x = 21.64 is the width
Find the cross sectional area
2.68 * 21.64 = 57.99 ~ 58
You can check it using the other solution.