Question

If $\sqrt{\left(1+\frac{27}{169}\right)}=\left(1+\frac{x}{13}\right)$, then $x$ equals ____________.

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is A $1$

Given, $\sqrt{1+\frac{27}{169}}=(1+\frac{x}{13})$

$\Rightarrow \sqrt{\frac{169+27}{169}}=(1+\frac{x}{13})$
$\Rightarrow \sqrt{\frac{196}{169}}=1+\frac{x}{13}$

$\Rightarrow \frac{14}{13}=1+\frac{x}{13}$

$\Rightarrow \frac{1}{13}=\frac{x}{13}$

$\Rightarrow x=1$