Question 316572: An open box is formed from a rectangular piece of cardboard, whose length is 3 inches more than it's width, by cutting 3 inch squares from each corner and folding up the sides. If the volume of the box is to be 264 in^2, find the size of the original piece of cardboard. What are the original dimensions of the piece of cardboard?
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! The original piece of cardboard has width of w and length of l=w+3
If you cut 3 inch squares from each side, you have to subtract 6 from each side (3 from each corner) to get the new dimensions:
L = (w+3-6)
W = w-6
H = 3 [ the height is 3 because when you fold up the cut corners, that gives you the height ]
Now we know that Volume = LxWxH, so let's plug everything in and solve for w:
V=LWH
264 = (w+3-6)(w-6)(3)
264 = 3(w-3)(w-6)
Do FOIL
264 = 3(w^2 -9w+18)
0 = 3w^2 -27w +54 - 264
0 = 3w^2 -27w -210
0 = 3(w^2 -9w -70)
Now you have to factor (think, what multiplies to -70 and has a difference of -9? Answer: -14 and 5.)
0 = 3(w-14)(w+5)
So we choose the positive answer, w=14.
This means the length is l=w+3 = 17
Width =14, Length =17
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