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 the sides. If the area of the base
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Question 188229: 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 the sides. If the area of the base is to be 80 square inches, then what size squares should be cut from each corner?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If x is the measure of the side of one of the cut out squares, then the length of the bottom of the box must be 14 - 2x, and the width must be 11 - 2x, so the area of the bottom of the box must be:
(11 - 2x) = 154 - 50x + 4x^2 = 80)
Putting the quadratic into standard form:
Divide by 2 to eliminate a common factor:
Use the quadratic formula:
 \pm sqrt{(-25)^2 - 4(2)(37)}}{2(2)})
You can do your own arithmetic from here, but you need to exclude one of the roots because it is too large. The larger answer is an extraneous root.
John
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