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 a cardboard and folding up the sides. If the area of the ba
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Question 186088: 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 a 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) (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 a 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?
;
Let x = the side of the square to cut from each corner
:
Draw a rough diagram of what is described, labeling the sides of the squares
as x and rectangular sheet as 11 by 14. It will be apparent to you that the
dimensions of the bottom of the box will be (11-2x) by (14-2x), which is given
as an area of 80 sq/in
:
(11-2x) * (14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
Arrange as a quadratic equation:
4x^2 - 50x + 154 - 80 = 0
:
4x^2 - 50x + 74 = 0
Simplify, divide by 2:
2x^2 - 25x + 37 = 0
:
Use the quadratic formula to find x
in this problem a=2, b=-25, c=37
:
:
Two solutions
x =
x = 10.784
and
x =
x = 1.712 inch squares, This is the only solution that makes sense here.
:
:
Check solution. 2 * 1.712 = 3.43, subtract from the original dimensions and
find the area
(11-3.43) * (14-3.43) =
7.57 * 10.57 = 80.0 sq/in confirms our solution
