Solve frac{sqrt{5}}{2*sqrt{5}}=frac{sigma_{c}}{1*10^5}

$$\frac { \sqrt { 5 } } { 2 \times \sqrt { 5 } } = \frac { \sigma _ { c } } { 1 \times 10 ^ { 5 } }$$

Solve for σ_c

$$\sigma _{c}=50000$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt{5}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}=\frac{\sigma _{c}}{1\times 10^{5}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}\sqrt{5}}{2\times 5}=\frac{\sigma _{c}}{1\times 10^{5}}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5}{2\times 5}=\frac{\sigma _{c}}{1\times 10^{5}}$$

Multiply 2 and 5 to get 10.

$$\frac{5}{10}=\frac{\sigma _{c}}{1\times 10^{5}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}=\frac{\sigma _{c}}{1\times 10^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{1}{2}=\frac{\sigma _{c}}{1\times 100000}$$

Multiply 1 and 100000 to get 100000.

$$\frac{1}{2}=\frac{\sigma _{c}}{100000}$$

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

$$\frac{\sigma _{c}}{100000}=\frac{1}{2}$$

Multiply both sides by 100000.

$$\sigma _{c}=\frac{1}{2}\times 100000$$

Multiply \frac{1}{2} and 100000 to get \frac{100000}{2}.

$$\sigma _{c}=\frac{100000}{2}$$

Divide 100000 by 2 to get 50000.

$$\sigma _{c}=50000$$