how do i found the the height

The volume of a rectangular box is (x^3+6x^2+11x6). The

box is (x+3) cm long and (x+2) cm wide. How high is the box?

May I also add that this is in the long division section of the text book so i am assuming i will have to apply long division in it somewhere, i actually do not understand where to start, I am not looking for an answer, just ways that i can tackle the problem. thank you.

Re: how do i found the the height

Quote:

Originally Posted by

**waleedrabbani** The volume of a rectangular box is (x^3+6x^2+11x6). The

box is (x+3) cm long and (x+2) cm wide. How high is the box?

May I also add that this is in the long division section of the text book so i am assuming i will have to apply long division in it somewhere, i actually do not understand where to start, I am not looking for an answer, just ways that i can tackle the problem. thank you.

Divide the volume by (x+3).

You should get a reminder of zero.

Take the quotient and divide by (x+2) .

You should get a reminder of zero.

That quotient is the height.

Re: how do i found the the height

Quote:

Originally Posted by

**waleedrabbani** The volume of a rectangular box is (x^3+6x^2+11x6). The

box is (x+3) cm long and (x+2) cm wide. How high is the box?

May I also add that this is in the long division section of the text book so i am assuming i will have to apply long division in it somewhere, i actually do not understand where to start, I am not looking for an answer, just ways that i can tackle the problem. thank you.

As an alternative, for any prism I always remember that the volume is equal to the cross-sectional area multiplied by the height.

You are told the length is $\displaystyle \displaystyle \begin{align*} x + 3 \end{align*}$ and the width is $\displaystyle \displaystyle \begin{align*} x + 2 \end{align*}$, so the cross sectional area is $\displaystyle \displaystyle \begin{align*} (x + 3)(x + 2) = x^2 + 5x + 6 \end{align*}$.

Therefore, you have

$\displaystyle \displaystyle \begin{align*} V &= AH \\ x^3 + 6x^2 + 11x + 6 &= \left(x^2 + 5x + 6\right)H \\ H &= \frac{x^3 + 6x^2 + 11x + 6}{x^2 + 5x + 6} \end{align*}$

Now perform this long division to simplify the height :)