SOLUTION: Please help me solve this: A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is
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Question 887311: Please help me solve this: A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is to be formed by cutting squares that measure 2 cm on each side from the 4 corners, and then folding up the sides. If the volume of the box will be 182 cm^3, what are the dimensions of the piece of cardboard? Found 2 solutions by josgarithmetic, MathTherapy:Answer by josgarithmetic(39617) (Show Source):
The height is the 2 cm length cut at each corner so that the flaps folded give height of 2 cm.
VOLUME is BaseArea*Height.
Simplify into general form equaling zero. Look for roots. It may be a bit of work finding the possible roots to check; but the roots must be positive, and you should try the smaller ones first. Not TOO small, since you had some described restrictions of "2" and "6". You need your x to be of sizes which make sense.
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-----Very few roots to try.
Try checking for 7, 14, 26,... still try checking 2 or 1, since this may give simpler resulting polynomial to check. (Rational Roots Theorem)
There must be a mistake in some of the work and discussion I just gave, because I tried the indicated synthetic divisions (most of them) and found no roots yet. I am assuming the roots must all be rational. Using the graphing feature in google, the one single root appears to be slightly less than 7. This root is about 6.9362....
You can put this solution on YOUR website! Please help me solve this: A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is to be formed by cutting squares that measure 2 cm on each side from the 4 corners, and then folding up the sides. If the volume of the box will be 182 cm^3, what are the dimensions of the piece of cardboard?
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