# Ex.6.5 Q17 Triangles Solution - NCERT Maths Class 10

## Question

Tick the correct answer and justify : In \(\Delta ABC\), \(AB =\) \(6\sqrt{3}\,\text{cm}\) , \(AC =\) \(12 \;\rm{}cm\) and \(BC =\) \(6 \;\rm{}cm\). The angle \(B\) is

(A) \(120^\circ\)

(B) \(60^\circ\)

(C) \(90^\circ\)

(D) \(45^\circ\)

## Text Solution

**Reasoning:**

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

**Steps:** **( c)**

In \(\Delta ABC\)

\[\begin{align}AB&=6 \sqrt{3} \mathrm{cm} ;\\ AC&=12 \mathrm{cm} ; \\ BC & =6 \mathrm{cm} \\ \\ A B^{2}&=108 \mathrm{cm}^{2} ; \\ AC^{2} & =144 \mathrm{cm}^{2} ; \\ BC^{2} & =36 \mathrm{cm}^{2} \\\\ A B^{2}+B C^{2}&=(108+36) \mathrm{cm}^{2} \\ \quad&=144 \mathrm{cm}^{2} \\ \Rightarrow A C^{2}&=A B^{2}+B C^{2}\end{align}\]

Pythagoras theorem is satisfied

\[\Rightarrow \angle ABC={{90}^{\circ}}\]