If 1 + x169 = 1413 , then x is equal to ?

Answer: Option C

$$\begin{array}{rl}& \Rightarrow \sqrt{1+\frac{x}{169}}=\frac{14}{13}\\ & \Rightarrow 1+\frac{x}{169}=\frac{196}{169}\\ & \Rightarrow \frac{x}{169}=\left(\frac{196}{169}-1\right)\\ & \Rightarrow \frac{x}{169}=\frac{27}{169}\\ & \Rightarrow x=27\end{array}$$