Question

In $\Delta PQR,PQ=6cm,PR=9cm$ and M is a point on QR such that it divides QR in the ratio 1 : 2 and PM $\perp$ QR. Find the length of QR.

Answer 1

$\Rightarrow QR=\sqrt{Q{P}^2+P{R}^2}$

When,

$\begin{array}{c}QR=QM+MR\\ QM=x-1\\ MR=x-2\\ QR=\sqrt{6^2+9^2}\\ =\sqrt{36+81}\\ QR=\sqrt{117}=10.82\end{array}$

From Question:

$\begin{array}{c}x-1+x-2=10.82\\ 2x-3=10.82\\ x=\frac{13.82}{2}\\ \Rightarrow QR=6.91\end{array}$