SOLUTION: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a si

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Question 964452: A rectangular piece of cardboard is to be formed into an uncovered box. The piece of cardboard is 2 centimeters longer than it is wide. A square that measures 3 centimeters on a side is cut from each corner. When the sides are turned up to form the box, its volume is 765 cubic centimeters. Find the dimensions, in centimeters, of the original piece of cardboard.
width = cm
length = cm


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of the bottom of the box is given by:
765cm%5E3%2F3cm=255cm%5E2
The length of the box is still 2 cm longer than the width.
W%5Bb%5D=box+width; L%5Bb%5D=box+length=W%5Bb%5D%2B2cm; A%5Bb%5D=box+area
A%5Bb%5D=L%5Bb%5DW%5Bb%5D Substitute for L%5Bb%5D
255cm%5E2=%28W%5Bb%5D%2B2cm%29%28W%5Bb%5D%29Subtract 255cm^2 from each side.
0=W%5Bb%5D%5E2%2B2W%5Bb%5D-255
0=%28W%5Bb%5D%2B17%29%28W%5Bb%5D-15%29
W%5Bb%5D%2B17=0 or W%5Bb%5D-15=0
W%5Bb%5D=-17 or W%5Bb%5D=15
Width of the box is 15cm
Length of box=width+2cm=17cm
The original cardboard is 6cm longer (3cm folded up on each end)
and 6cm wider (3cm folded up on each side)so:
L%5Bb%5D%2B6cm=17cm%2B6cm=23cm ANSWER 1: The cardboard rectangle was 23 cm long.
W%5Bb%5D%2B6cm=15cm%2B6cm=21cm ANSWER 2: The cardboard rectangle was 21 cm wide.