You can
put this solution on YOUR website!Thomas is going to make an open top box by cutting equal squares from the four corners of an 11 inch by 14 inch piece of cardboard and folding up the 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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Regarding you answer; 2.45 by 1.5 is not a square
Here's how I would do it:
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Let x = side of the square to be cut out, it will also be the height of the box
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Since the base has to be 80 sq/in then the volume would be 80x
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Height * width * length = 80x
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x * (11-2x)*(14-2x) = 80x
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Divide both sides by x, it will be a simple quadratic equation then
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(11-2x)*(14-2x) = 80
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154 - 50x + 4x^2 = 80
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4x^2 - 50x + 154 - 80 = 0
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4x^2 - 50x + 74 = 0
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Simplify, divide by 2
2x^2 - 25x + 37 = 0
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Using the quadratic formula; a=2; b=-25; c=37
I got: x = +10.78; and x = +1.715; this is the logical solution
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the side of the squares to be cut out will be 1.715 inches.
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Check the area of the base to confirm our solution of x = 1.715 inches:
Find 2x: 2 * 1.715 = 3.43
(11 - 3.43) * (14 - 3.43) =
7.57 * 10.57 = 80.015 ~ 80 sq inches
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Do you get it now?
