SOLUTION: Hi, I need help with this question, it's really confusing: "A rectangular piece of cardboard is twice as long as it is wide. A four-centimeter square is cut out of each corner,

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Question 1120793: Hi, I need help with this question, it's really confusing:
"A rectangular piece of cardboard is twice as long as it is wide. A four-centimeter square is cut out of each corner, then the sides are turned up to
make a box. The volume of the box is 616 cubic centimeters. Find the original
dimensions of the rectangular piece of cardboard."
Thanks!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions of the original cardboard:
x and 2x

Cutting out the 4 cm corners means that the box height formed is 4 cm.

Dimensions of the bottom of box:
x-2%2A4 and 2x-2%2A4


Volume given as 616 cubic cm.

highlight_green%284%28x-8%29%282x-8%29=616%29
Simplify and solve this.

%28x-8%29%282x-8%29=154
%28x-8%29%2A2%2A%28x-4%29=154
%28x-8%29%28x-4%29=77

Notice on the left side, the two factors differ by 4; and see on the right side, the product 77 could be 7%2A11.
Those are the factors you want.
(or you could have gone ahead, multiplied, and use either factorization or quadratic formula solution.)

x-8=7
highlight%28x=15%29---------width

x-4=11
x=11%2B4
highlight%28x=15%29--------width

Length would be highlight%2830%29.