Question

Let $S_1,S_2$ are foci of an ellipse, whose major axis length is $15$ units and $P$ be any point on the ellipse such that perimeter of triangle $P{S}_1{S}_2$ is $20$ units. If $e$ is the eccentricity of the ellipse, then $3e=$

Answer 1

Given, $2a=15$
and $P{S}_1+P{S}_2+S_1{S}_2=20$
$\Rightarrow 2a+2ae=20$
$\Rightarrow 2a(1+e)=20$
$\Rightarrow 15(1+e)=20$
$\Rightarrow 3e=1$