Tick the correct answer and justify :
Question.

Tick the correct answer and justify : In $\Delta \mathrm{ABC}, \mathrm{AB}=6 \sqrt{3} \mathrm{~cm}, \mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{BC}=6 \mathrm{~cm}$. The angle $\mathrm{B}$ is :

(1) 120°

(2) 60°

(3) 90°

(4) 45°

Solution:

$\mathrm{AB}^{2}=(6 \sqrt{3})^{2}=108$

$\mathrm{BC}^{2}=6^{2}=36$

$A C^{2}=12^{2}=144$

So, $\mathrm{AB}^{2}+\mathrm{BC}^{2}=\mathrm{AC}^{2}$

$\Delta \mathrm{ABC}$ is right $\Delta$, right angled at $\mathrm{B}$

$\angle \mathrm{B}=90^{\circ}$
Editor