Question 1146037
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The volume of the box is length times width times height.  The height is 3 inches, and the volume is 135 cubic inches.  So the length times the width is 135/3 = 45.<br>
When the 3-inch square pieces are cut out of each corner, the new length is still 12 inches more than the new width.<br>
So we can solve the problem simply by finding two numbers that differ by 12 and whose product is 45.<br>
A bit of mental arithmetic shows those two numbers to be 3 and 15.  Then, since 3-inch square pieces were cut out of each corner of the piece of cardboard, the dimensions of the piece of cardboard were 3+6=9 and 15+6=21.<br>
ANSWER: The piece of cardboard was 21x9 inches.<br>
You can, of course, solve the problem using formal algebra.<br>
x = width
x+12 = length<br>
The volume is 135 after cutting out 3-inch squares from each corner:<br>
{{{3(x-6)((x+12)-6) = 135}}}
{{{3(x-6)(x+6) = 135}}}
{{{(x-6)(x+6) = 45}}}
{{{x^2-36 = 45}}}
{{{x^2 = 81}}}
{{{x = 9}}}<br>
ANSWER:
width = x = 9
length = x+12 = 21