If the eccentricity and length of latusrectum of a hyperbola are $\frac{\sqrt{13}}{3}$ and $\frac{10}{3}$
respectively then length of transverse axis is

Given $\mathrm{e}=\frac{\sqrt{13}}{3},$ and $\frac{2{\mathrm{b}}^2}{\mathrm{a}}=\frac{10}{3}$

$$\begin{gathered} \Rightarrow 3{\mathrm{b}}^2=5\mathrm{a} \\ \Rightarrow 3{\mathrm{a}}^2({\mathrm{e}}^2-1)=5\mathrm{a} \\ \Rightarrow 3\mathrm{a}\left(\frac{13}{9}-1\right)=5 \\ \Rightarrow 3\mathrm{a}\times \frac{4}{9}=5 \\ \Rightarrow \mathrm{a}=\frac{15}{4} \end{gathered}$$

$\therefore$Length of transverse axis $=2\mathrm{a}$

$=\frac{15}{2}$