SOLUTION: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up sides. If the area of the base is
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Question 99493: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
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Draw a rectangle 14 by 11, label the side of the squares cut out on the corners as x.
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It will be apparent that the box dimension will be (14-2x) by (11-2x) by x
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The base area is given as 80.
(14-2x) * (11-2x) = 80
FOIL
154 - 28x - 22x + 4x^2 = 80
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A quadratic equation:
4x^2 - 50x + 154 - 80 = 0
:
4x^2 - 50x + 74 = 0
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Simplify, divide by 2:
2x^2 - 25x + 37 = 0
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Solve for x using the quadratic formula: a = 2, b= -25, c = 37
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Two solutions:
x = 10.78 inches, obviously not a solution
and
x = 1.71 inches, the side of the removed squares
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Check solution by finding the area of the box dimensions:
2x: 2(1.71) = 3.42
(14 - 3.42) * (11 - 3.42) =
10.58 * 7.58 = 80.2 ~ 80, confirms our solution
