Question

If $\frac{52}{x}=\sqrt{\frac{169}{289}}$, then $x=68$.

• A. True
• B. False

Answer 1

The correct option is A True

Solve the given equation for $x$ by using the law of exponent.

$\begin{array}{l}\frac{52}{x}=\sqrt{\frac{169}{289}}\\ \Rightarrow \frac{52}{x}=\sqrt{\frac{{13}^2}{{17}^2}}\\ \Rightarrow \frac{52}{x}=\frac{13}{17}\\ \Rightarrow 13x=52\times 17\left[\mathrm{cross}\mathrm{multiplication}\right]\\ \Rightarrow x=\frac{52\times 17}{13}\\ \Rightarrow x=68\end{array}$

Hence, the given statement is true.