Question

In the given figure, find $PM$.

• A. $2cm$
• B. $3cm$
• C. $4cm$
• D. $5cm$

Answer 1

The correct option is C

$4cm$

Explanation for the correct option:

Find the length of $PM$

In the $△POL$,

$\angle OLP=90°$, by Pythagoras' theorem

$\begin{array}{rcl}{\left(OL\right)}^2+{\left(LP\right)}^2& =& {\left(OP\right)}^2\\ \Rightarrow {\left(3\right)}^2+{\left(LP\right)}^2& =& {\left(5\right)}^2\\ \Rightarrow {\left(LP\right)}^2& =& 16\\ \Rightarrow LP& =& 4cm\end{array}$

In $△POL$and $△POM$, $PO$ is common,

$\angle LOP=\angle MOP$ (Given)

$\angle OLP=\angle OMP=90°$

$△POL\cong △POM$ $(byAAS)$

$PL=PM=4cm$ (by Corresponding parts of congruent triangles theorem)

Hence, the length of $PM$ is $4cm$.

Hence, option (C) is correct answer.