Question

$PQR$ is a triangle, right angled at $P$. If $PQ=10cm$ and $PR=24cm$, find $QR$.

Answer 1

Given:

In figure,

$PQ=10cm$, $PR=24cm$

Let $QR$ be $xcm$.

In right angled triangle $PQR$,

By Pythagoras theorem,

Square of the hypotenuse is equal to sum of the squares of the other two sides.

$\Rightarrow {\text{(Hypotenuse)}}^2={\text{(Base)}}^2+{\text{(Perpendicular)}}^2$

$\Rightarrow (QR{)}^2=(PQ{)}^2+(PR{)}^2$

$\Rightarrow x^2=(10cm{)}^2+(24cm{)}^2$

$\Rightarrow x^2=100c{m}^2+576c{m}^2=676c{m}^2$

$\Rightarrow x=\sqrt{676c{m}^2}=26cm$

Thus, the length of $QR$ is $26cm$.