SOLUTION: Identical squares are cut from each corner of an 8 inch by 11.5 inch rectangular piece of cardboard.The sides are folded up to make a box with no top .If the volume of the resultin

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Question 983709: Identical squares are cut from each corner of an 8 inch by 11.5 inch rectangular piece of cardboard.The sides are folded up to make a box with no top .If the volume of the resulting box is 63.75 cubic inches,how long is the edge of each square that is cut off ?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
u, edge of each identical cut-out square
w, width of rectangular cardboard
L, length of cardboard
v, volume of the open-top box

The box is u tall and the base is (w-2u)(L-2u).
The volume is highlight_green%28%28w-2u%29%28L-2u%29%2Au=v%29.

Solve for u.

%28wL-2uL-2uw%2B4u%5E2%29u=v
4u%5E3-2Lu%5E2-2wu%5E2%2BwLu-v=0
highlight_green%284u%5E3-%282L%2B2w%29u%5E2%2BwLu-v=0%29-----Now we need to plug-in the known values for the cubic equation.

4u%5E3-39u%5E2%2B92u-63.75=0
Integers are preferred so multiply by 4...
cross%2816u%5E4-156u%5E2%2B368u-255=0%29---possibly wrong - did not work-

The roots (if Rational Roots Theorem) we want must be positive but certainly much less than 8. Most sensible to first check for 1 and 3 (both are factors of 255).

I used a graphing tool.
... graph shows roots at u=1.5 and u=1.6.