Question

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

Answer 1

Step 1. Draw a rough figure of $△PQR$.

From the above figure, $\overline{PQ}$ $=$$10cm$ and $\overline{PR}$ $=24cm$.

Step 2. Find $\overline{\mathbf{QR}}$ by using the Pythagoras theorem.

As, $\angle QPR={90}^o$, using Pythagoras theorem, ${\left(\overline{QR}\right)}^2={\left(\overline{PQ}\right)}^2+{\left(\overline{PR}\right)}^2$.

Put the values of the given sides, ${\left(\overline{QR}\right)}^2={\left(10\right)}^2+{\left(24\right)}^2=100cm+576cm$

${\left(\overline{QR}\right)}^2=676cm$

$\overline{QR}$ $=\sqrt{676}$

$\overline{QR}$$=26cm$.

Hence, the required length of $\overline{QR}$ is $26cm$.