Question

In the figure: $\angle PSQ={90}^0,PQ=10cm,QS=6cm$ and $RQ=9cm$. Calculate the length of $PR$ (in cm).

Answer 1

Since, $△PQS$ is a right angled triangle , we have
${PQ}^2={PS}^2+{SQ}^2$
$\Rightarrow {10}^2={PS}^2+6^2$
$\Rightarrow {PS}^2=100-36=64$
$\Rightarrow PS=8cm$
Similarly, as $△PRS$ is a right angled triangle , we have
${PR}^2={PS}^2+{SR}^2$
$\Rightarrow {PR}^2=8^2+{(6+9)}^2$
$\Rightarrow {PR}^2=64+225=289$
$\Rightarrow PR=17cm$