Question

The formula for the surface area s of a rectangular prism is s=2lw+2lh+2wh. Solve the formula for the height h.

Answer 1

Let's solve the surface area for the height:

$\begin{gathered} s=2lw+2lh+2wh \\ s-2lw=2h(l+w) \\ 2h=\frac{s-2lw}{l+w} \\ h=\frac{s-2lw}{2(l+w)} \end{gathered}$

Therefore, the expression for the height is:

$h=\frac{s-2lw}{2(l+w)}$