Find x from the following:$\sqrt{1+\frac{27}{169}} = 1+ \frac{x}{13}$

Given :

The given expression is $\sqrt{1+\frac{27}{169}} = 1+ \frac{x}{13}$.

To do :

We have to find the value of x.

Solution :

$\sqrt{1+\frac{27}{169}} = 1+ \frac{x}{13}$

$\Longrightarrow \sqrt{\frac{169 +27}{169}} = 1+ \frac{x}{13}$

$\Longrightarrow \sqrt{\frac{196}{169}} = 1+ \frac{x}{13}$

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

$\Longrightarrow \frac{14}{13} -1=  \frac{x}{13}$

$\Longrightarrow \frac{14-13}{13} =  \frac{x}{13}$

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

Rewrite,

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

$\Longrightarrow x = 1$.

The value of x is 1.

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Updated on: 10-Oct-2022

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