SOLUTION: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base

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Question 80882: Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11inch 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 square should be cut from each corner?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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 sheet 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?
:
Draw rough diagram of this, a rectangle 11 by 14, with squares cut out at each
corner. Label the side of these squares as x. It will be apparent to you that
the dimensions of the base will be (11-2x) by (14-2x). It's area is given as 80
:
A simple area equation:
(11-2x) * (14-2x) = 80
FOIL
154 - 50x + 4x^2 = 80
:
4x^2 - 50x + 154 - 80 = 0
:
4x^2 - 50x + 74 = 0
:
Not easily factored, so use the quadratic formula: a=4, b=-50, c=74
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-50%29+%2B-+sqrt%28-50%5E2-4%2A4%2A74+%29%29%2F%282%2A4%29+
x+=+%28%2B50+%2B-+sqrt%28+2500+-+1184%29%29%2F%288%29+
x+=+%28%2B50+%2B-+sqrt%281316%29%29%2F%288%29+
x+=+%28%2B50+%2B-+36.2767%29%2F%288%29+
Two solutions:
x+=+%28%2B50+%2B+36.2767%29%2F%288%29+
x+=+%28%2B86.2767%29%2F%288%29+
x = +10.78
and
x+=+%28%2B50+-+36.2767%29%2F%288%29+
x+=+%28%2B13.7232%29%2F%288%29+
x = +1.715
:
The smaller solution is the only one that makes sense:
A 1.715 inch square should be cut from each corner
:
:
Check our solution by finding the area of the base with these dimensions:
Find 2x: 2*1.715 = 3.43
(11 - 3.43) * (14 - 3.43) = 80.01 ~ 80 sq in
:
How about this? Did it seem logical and understandable to you?