Solve frac{sqrt{3}}{3}=frac{frac{sqrt{2}}{2}}{1/h}

$$\frac { \sqrt { 3 } } { 3 } = \frac { \frac { \sqrt { 2 } } { 2 } } { \frac { 1 } { h } }$$

Solve for h

$$h=\frac{\sqrt{6}}{3}\approx 0.816496581$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$\sqrt{3}=3h\times \frac{\sqrt{2}}{2}$$

Express 3\times \frac{\sqrt{2}}{2} as a single fraction.

$$\sqrt{3}=\frac{3\sqrt{2}}{2}h$$

Express \frac{3\sqrt{2}}{2}h as a single fraction.

$$\sqrt{3}=\frac{3\sqrt{2}h}{2}$$

Multiply both sides of the equation by 2.

$$2\sqrt{3}=3\sqrt{2}h$$

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

$$3\sqrt{2}h=2\sqrt{3}$$

Divide both sides by 3\sqrt{2}.

$$\frac{3\sqrt{2}h}{3\sqrt{2}}=\frac{2\sqrt{3}}{3\sqrt{2}}$$

Dividing by 3\sqrt{2} undoes the multiplication by 3\sqrt{2}.

$$h=\frac{2\sqrt{3}}{3\sqrt{2}}$$

Divide 2\sqrt{3} by 3\sqrt{2}.

$$h=\frac{\sqrt{6}}{3}$$