Question

$ABC$ is a triangle, right-angled at $C$. If $\overline{AB}$ $=25cm$ and $\overline{AC}$ $=7cm$ find $\overline{BC}$.

Answer 1

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

From the above figure, $\overline{AC}$ $=7cm$ and $\overline{AB}$ $=25cm$.

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

Using the Pythagoras theorem, ${\left(\overline{AB}\right)}^2={\left(\overline{AC}\right)}^2+{\left(\overline{BC}\right)}^2$

${\left(\overline{BC}\right)}^2={\left(\overline{AB}\right)}^2-{\left(\overline{AC}\right)}^2$.

${\left(\overline{BC}\right)}^2={\left(25\right)}^2-{\left(7\right)}^2$

${\left(\overline{BC}\right)}^2=625-49$

${\left(\overline{BC}\right)}^2=576$

$\left(\overline{BC}\right)=\sqrt{576}$

$\overline{BC}$ $=24cm$

Hence, the required length of $\overline{BC}$ is $24cm$.