Solve a/sqrt{3/2}=20/sqrt{2/2}

$$\frac { a } { \frac { \sqrt { 3 } } { 2 } } = \frac { 20 } { \frac { \sqrt { 2 } } { 2 } }$$

Solve for a

$$a=10\sqrt{6}\approx 24.494897428$$

Steps for Solving Linear Equation

Divide a by \frac{\sqrt{3}}{2} by multiplying a by the reciprocal of \frac{\sqrt{3}}{2}.

$$\frac{a\times 2}{\sqrt{3}}=\frac{20}{\frac{\sqrt{2}}{2}}$$

Rationalize the denominator of \frac{a\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{a\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}=\frac{20}{\frac{\sqrt{2}}{2}}$$

The square of \sqrt{3} is 3.

$$\frac{a\times 2\sqrt{3}}{3}=\frac{20}{\frac{\sqrt{2}}{2}}$$

Divide 20 by \frac{\sqrt{2}}{2} by multiplying 20 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{a\times 2\sqrt{3}}{3}=\frac{20\times 2}{\sqrt{2}}$$

Multiply 20 and 2 to get 40.

$$\frac{a\times 2\sqrt{3}}{3}=\frac{40}{\sqrt{2}}$$

Rationalize the denominator of \frac{40}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{a\times 2\sqrt{3}}{3}=\frac{40\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{a\times 2\sqrt{3}}{3}=\frac{40\sqrt{2}}{2}$$

Divide 40\sqrt{2} by 2 to get 20\sqrt{2}.

$$\frac{a\times 2\sqrt{3}}{3}=20\sqrt{2}$$

Multiply both sides of the equation by 3.

$$a\times 2\sqrt{3}=60\sqrt{2}$$

The equation is in standard form.

$$2\sqrt{3}a=60\sqrt{2}$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}a}{2\sqrt{3}}=\frac{60\sqrt{2}}{2\sqrt{3}}$$

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

$$a=\frac{60\sqrt{2}}{2\sqrt{3}}$$

Divide 60\sqrt{2} by 2\sqrt{3}.

$$a=10\sqrt{6}$$