Question

In the figure.: $\angle PSQ={90}^{\circ },PQ=10cm,QS=6cm$ and $RQ=9cm$. Calculate the length of PR (in cm).

Answer 1

Given: $\angle PSQ={90}^{\circ }$ $PQ=10$ cm, $QS=6$ cm and $RQ=9$ cm

In $△PQS$,
$P{Q}^2=P{S}^2+S{Q}^2$ (Pythagoras theorem)
${10}^2=P{S}^2+6^2$
$P{S}^2=100-36$
$P{S}^2=64$
$PS=8$ cm
Now, In $△PRS$,
$P{R}^2=P{S}^2+R{S}^2$ (Pythagoras theorem)
$P{R}^2=P{S}^2+(RQ+QS{)}^2$
$P{R}^2=8^2+{15}^2$
$P{R}^2=64+225$
$P{R}^2=289$
$PR=17$ cm