A rectangular box has sides with lengths x, x+1, and x+2. If the volume of the box is 504 cubic inches, find the dimensions of the box.

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- Jul 16th 2009, 01:56 PMmoomoo762Someone please help solve this problem
A rectangular box has sides with lengths x, x+1, and x+2. If the volume of the box is 504 cubic inches, find the dimensions of the box.

- Jul 16th 2009, 02:19 PMskeeter
- Jul 16th 2009, 02:19 PMyeongil
You should know that the formula for the volume of a rectangular prism is

V = LWH.

So plug in:

(let's switch sides)

Multiply out the left side, and afterwards, subtract 504 from both sides. You'll end up with a cubic equation equaling zero. Solve for x. Don't forget to reject any solution that gives you a negative number for**any**of the lengths.

01

EDIT: beaten to it by skeeter! (Rofl) - Jul 16th 2009, 02:45 PMmoomoo762
I'm stuck

I subtract 504 from both sides to make it equal to zero and I get

x^3+5x^2+2x-504=0

What's the best way to solve for x now? - Jul 16th 2009, 03:12 PMskeeter
- Jul 16th 2009, 03:30 PMmoomoo762
Using the rational root test I got 7

I know the other two sides are 8 and 9 but how do I go about finding them? - Jul 16th 2009, 04:21 PMskeeter
first of all, correct your expansion ...

you know 7 is a root ... use synthetic division

Code:`7] 1.......3........2.......-504`

............7.......70........504

-------------------------------

....1......10.......72.........0

since , the other two roots are imaginary.

is the only real root

go back to the original equation ...

- Jul 16th 2009, 04:24 PMStroodle

Notice that there are no real solutions for the quadratic factor as

So the only real solution is

The question stated the sides are so one side is and the others are and