Question

In $△PQR$, M is the midpoint of side QR. If PQ is $11$ cm, PR is $17$ cm and QR = $12$ cm, find PM.

• A. $15$ cm
• B. $13$ cm
• C. $17$ cm
• D. $23$ cm

Answer 1

The correct option is B $13$ cm

In $△PQR$,

M is the midpoint of side QR ........ given

$\therefore$ PM is the median of the triangle.

By Apollonius theorem,

${PQ}^2+{PR}^2=2{PM}^2+2{QM}^2$

${11}^2+{17}^2=2P{M}^2+2{\left(\frac{1}{2}QR\right)}^2$

$121+289=2P{M}^2+2(6{)}^2$

$410=2P{M}^2+72$

$2P{M}^2=338$

$P{M}^2=169$

$\therefore PM=13$ cm ........Taking sq. roots

So, option B is correct.