SOLUTION: An open box is made from a rectangular piece of cardboard whose length is twice the width, by cutting a 3 inch square from each corner and folding up the remaining sides. Find the
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Question 811373: An open box is made from a rectangular piece of cardboard whose length is twice the width, by cutting a 3 inch square from each corner and folding up the remaining sides. Find the dimensions of the box if the volume is 648 cubic inches Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website! Width = x
Length = 2x
Cutting 3 inch square from each corner:
Width = x - 6
Length = 2x - 6
Volume of rectangular box
= length * width * height
= (2x - 6)*(x - 6)*(3) = 648
= 6x^2 - 54x + 108 = 648
= 6x^2 - 54x - 540 = 0
Divide thro'out by 6
= x^2 - 9x - 90 = 0
= (x + 6)(x - 15)= o
x = -6 (no answer as x < 0)
x = 15 inches.
Width = 9 inches
Length = 24 inches.
Height = 3 inches.
Hope this helps.
:-)
