Answer : $\large\frac{4}{\sqrt 3}$
Equation of the ellipse is $3x^2+y^2=12$
(ie) $\large\frac{x^2}{4}+\frac{y^2}{12}$$=1$
$\Rightarrow a^2=4$ or $a=2$
$b^2=12$ or $b=\sqrt{12}$
Length of the latus rectum =$\large\frac{2a^2}{b}$
$\Rightarrow \large\frac{2\times 4}{\sqrt{12}}$
$\Rightarrow \large\frac{4}{\sqrt 3}$
The length of the latus rectum of the ellipse $3x^2+y^2=12$ is $\large\frac{4}{\sqrt 3}$