Question 259875: Open-top box. 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?
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 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 4 squares to be cut from each corner
then the dimensions of the base will be:
(11-2x) by (14-2x)
:
Given the area, we have:
(11-2x)*(14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
:
4x^2 - 50x + 154 - 80 = 0
:
A quadratic equation
4x^2 - 50x + 74 = 0
;
simplify divide by 2
2x^2 - 25x + 37 = 0
;
Solve this using the quadratic formula; a=2; b=-25, c=37
you should get the reasonable answer of
x = 1.715 inches is the side of the removed squares
:
:
Check this on a calc: enter (11-2(1.715)) * (14-2(1.715)) = 80.015 ~ 80
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