SOLUTION: Thomas is going to make an open-tpo box by cutting equal suqres from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the base is to be 80

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Question 122535: Thomas is going to make an open-tpo box by cutting equal suqres from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the base is to be 80 square inches, then what size suqare should be cut from each corner?
Answer by ankor@dixie-net.com(22740) (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 base is to be 80 square inches, then what size square should be cut from each corner?
:
Draw a rectangle; label the sides 11" and 14"; label the sides of the squares on
the corners as x. I will be apparent that dimension of the box will be:
(11-2x) by (14-2x) by x(height). The base area is given as 80 sq/in, therefore:
:
(11-2x) * (14-2x) = 80
FOIL
154 - 22x - 28x + 4x^2 = 80
:
Arrange as a quadratic equation on the left:
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: a=2; b=-25; c=37

Two solutions

x = 10.78; obviously this is not the solution
Solution 2:

x = 1.7155 inches; this solution makes sense (side of the square to be removed)
:
:
Check solution by find the area of the base: 2x = 3.431
(11-3.431)*(14-3.431) = 79.9967 ~ 80