Question 817309: Please help! :-)
A rectangular piece of cardboard has a length 3 inches less than twice the width. A square 3 inches on a side is cut out of each corner and the sides are turned up to form an open box with a volume of 132 in^3. Find the dimensions of the unfinished box.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! volume (V) = 132
V = 132 = (2w -3) * w * 3
132 = 6w^2 -9w
put equation into standard form
6w^2 -9w -132 = 0
use quadratic formula to solve
w = (-(-9) + square root( (-9)^2 -4*6*(-132))) / (6*2)
w = (-(-9) - square root( (-9)^2 -4*6*(-132))) / (6*2)
w = 5.5 and -4
w = 5.5 is the solution, therefore
l = 2*(5.5) -3 = 8 so,
length = 8 inches, width = 5.5 inches, height = 3 inches
check answer,
8 * 5.5 *3 = 132
132 = 132
answer checks
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