Question

ans this one..................​

Answer 1

Know that

$2\triangle PMN=\square ABCD$

$\triangle PQR -\triangle PMN=\square ABCD$

∴ $3\triangle PMN=\triangle PQR$

and

$\triangle PMN \sim \triangle PQR$ ( AA )

$\triangle PMN : \triangle PQR=1:3$

∴ Ratio of similarity is $1:\sqrt{3}$.

$\frac{MN}{QR} =\frac{1}{\sqrt{3} }$

∴ $\frac{MN}{QR} =\frac{\sqrt{3} }{3}$

$\frac{PM}{MQ} =\frac{1}{\sqrt{3} -1}$

∴ $\frac{PM}{MQ} =\frac{1+\sqrt{3} }{2}$