Question 80116This question is from textbook
: open top box thomas is going to make an open topbox by cutting equal squares from the four corners of an 11 inch by 14 inch peice 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?
I set it up like this but I think I am wrong
here goes:
80=14^2 2.45inches
80=11^2 1.5 inches
so my answer is 2.45 by 1.5 inches is this right if not please give me step by step because I just dont get it
This question is from textbook
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 piece 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?
;
Regarding you answer; 2.45 by 1.5 is not a square
Here's how I would do it:
:
Let x = side of the square to be cut out, it will also be the height of the box
:
Since the base has to be 80 sq/in then the volume would be 80x
:
Height * width * length = 80x
:
x * (11-2x)*(14-2x) = 80x
:
Divide both sides by x, it will be a simple quadratic equation then
:
(11-2x)*(14-2x) = 80
:
154 - 50x + 4x^2 = 80
:
4x^2 - 50x + 154 - 80 = 0
:
4x^2 - 50x + 74 = 0
:
Simplify, divide by 2
2x^2 - 25x + 37 = 0
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Using the quadratic formula; a=2; b=-25; c=37
I got: x = +10.78; and x = +1.715; this is the logical solution
:
the side of the squares to be cut out will be 1.715 inches.
:
Check the area of the base to confirm our solution of x = 1.715 inches:
Find 2x: 2 * 1.715 = 3.43
(11 - 3.43) * (14 - 3.43) =
7.57 * 10.57 = 80.015 ~ 80 sq inches
:
Do you get it now?
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