Question

In the given figure, the point O is situated within the triangle PQR in such a way that $\angle POQ={90}^{\circ }$, OP = 6 cm , OQ = 8 cm , If PR = 24 cm & $\angle QPR={90}^{\circ }$, then find the length of QR.

Answer 1

Using Pythagoras theorem in $△$POQ we get

$P{Q}^2=P{O}^2+O{Q}^{2}P{Q}^2=(6{)}^2+8^2=36+64=100PQ=10cm$

Using Pythagoras theorem in $△$ PRQ we get

$R{Q}^2=R{P}^2+P{Q}^{2}R{Q}^2=(24{)}^2+(10{)}^2\Rightarrow R{Q}^2=576+100\Rightarrow R{Q}^2=676\Rightarrow RQ=26cm$

Hence the length of QR will be equal to 26 cm.