Answer
$w+1$
Work Step by Step
We can start by setting the width as $w$. From the question, we can see that the length is $2w+5$. We are trying to solve for the height in terms of $w$.
Let's start by dividing the volume by $w$, the width:
$\frac{2w^3+7w^2+5w}{w}=\frac{w(2w^2+7w+5)}{w} = 2w^2+7w+5$.
We can divide this expression by the length, $2w+5$.
$\frac{2w^2+7w+5}{2w+5} = w+1$.
Because we know that $Volume = Width \cdot Length \cdot Height$, height has to be $w+1$ because we have divided the length and the width already.
Therefore, the height is $w+1$.
