SOLUTION: Sandy makes an open-top box by cutting equal squares from the corners of a rectangular piece of corrugated cardboard and folding up the sides. If the original piece measured 16 inc

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Question 884901: Sandy makes an open-top box by cutting equal squares from the corners of a rectangular piece of corrugated cardboard and folding up the sides. If the original piece measured 16 inches by 10 inches, and if the area of the box bottom is to be 216 in^2, what size square should Sandy cut from each corner?
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, solver91311:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the side length square to cut.
The bottom area will be highlight_green%28%2816-2x%29%2810-2x%29=216%29 and this ends my part of the response. Solve for x.


%2816-2x%29%2810-2x%29=216
160-20x-32x%2B4x%5E2=216
4x%5E2-52x%2B160=216
x%5E2-13x%2B40=54
x%5E2-13x-14=0
%28x%2B1%29%28x-14%29=0
highlight%28cross%28x=14%29%29----THIS IS IMPOSSIBLE! Not enough length on either dimension to cut a side of a square of 14 inches.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Sandy makes an open-top box by cutting equal squares from the corners of a rectangular piece of corrugated cardboard and folding up the sides.
If the original piece measured 16 inches by 10 inches, and if the area of the box bottom is to be 216 in^2, what size square should Sandy cut from each corner?
;
I don't think this will work, the area of the original piece is only 160 sq/in
How could you have a bottom with 216 sq/in???

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Not possible. If the original piece of cardboard measures 16 inches by 10 inches, the largest bottom box that could be created would be one that is 160 square inches, and that would presume you were allowed to make a box with ZERO height.

John

My calculator said it, I believe it, that settles it
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