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In ΔABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm, then ∠B is
1. 120°
2. 60°
3. 90°
4. 45°

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Correct Answer - Option 3 : 90°

Given:

AB, BC and AC are the three sides of ΔABC of length 6√3 cm, 6 cm and 12 cm respectively

Concept used:

If in a ΔABC, AB2 + BC2 = AC2

Then ΔABC is a rightangle triangle with ∠B = 90°

Calculation:

According to the concept, we have

 AB2 + BC2 = {(6√3)2 + 62} cm2

⇒ (108 + 36) cm2

⇒ 144 cm2      ----(1)

And, AC2 = 12cm2

⇒ 144 cm2      ----(2)

Here, equation (1) = equation(2)

So, AB2 + BC2 = AC2

∴ ∠B is 90°.

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