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

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## 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

$\Rightarrow \angle ABC={{90}^{\circ}}$

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