Solve m_{n}=1/2rho_{3}bh

$$m _ { n } = \frac { 1 } { 2 } \rho _ { 3 } b h$$

Solve for b

$$\left\{\begin{matrix}b=\frac{2m_{n}}{h\rho _{3}}\text{, }&h\neq 0\text{ and }\rho _{3}\neq 0\\b\in \mathrm{R}\text{, }&\left(\rho _{3}=0\text{ or }h=0\right)\text{ and }m_{n}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}\rho _{3}bh=m_{n}$$

The equation is in standard form.

$$\frac{h\rho _{3}}{2}b=m_{n}$$

Divide both sides by \frac{1}{2}\rho _{3}h.

$$\frac{2\times \frac{h\rho _{3}}{2}b}{h\rho _{3}}=\frac{2m_{n}}{h\rho _{3}}$$

Dividing by \frac{1}{2}\rho _{3}h undoes the multiplication by \frac{1}{2}\rho _{3}h.

$$b=\frac{2m_{n}}{h\rho _{3}}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{2m_{n}}{b\rho _{3}}\text{, }&b\neq 0\text{ and }\rho _{3}\neq 0\\h\in \mathrm{R}\text{, }&\left(\rho _{3}=0\text{ or }b=0\right)\text{ and }m_{n}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{2}\rho _{3}bh=m_{n}$$

The equation is in standard form.

$$\frac{b\rho _{3}}{2}h=m_{n}$$

Divide both sides by \frac{1}{2}\rho _{3}b.

$$\frac{2\times \frac{b\rho _{3}}{2}h}{b\rho _{3}}=\frac{2m_{n}}{b\rho _{3}}$$

Dividing by \frac{1}{2}\rho _{3}b undoes the multiplication by \frac{1}{2}\rho _{3}b.

$$h=\frac{2m_{n}}{b\rho _{3}}$$