Question 263025
A rain gutter is made from sheets of aluminum that are 20 inches wide. Determine the depth of the gutter that will allow a cross-sectional area of 13 square inches. Show that there are 2 different solutions to the problem. Round to the nearest tenth of an inch.
x(20+2x)= 13.
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The cross-section is a slice thru the gutter from top thru the bottom.
The shape is a "U".
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If height = base = x inches you get x^2 = 13 and x = sqrt(13)
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If base is x then height is (20-x)/2:
x(20-x)/2 = 13
20x - x^2 = 26
x^2 -20x + 26 = 0
x = [20 +- sqrt(400 - 4*1*26)]/2
x = [20 +- sqrt(296)]/2
x = [20 + 17.2]/2 = 37.2/2 = 18.6"
OR
x = [20 - 17.2]/2 = 1.4"
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So base could be 18.6 and height be (1.4/2) = 0.7"
Or base could be 1.4" and height be (18.6/2) = 9.3"
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Cheers,
Stan H.