Question

In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ______.

Options

• ∠A + ∠B = 60°

• ∠A + ∠B = 90°

• ∠A + ∠B = 120°

• ∠A + ∠B = 150°

Answer 1

In ΔABC, if (a+ b - c)(a + b + c) = 3ab, then ∠A + ∠B = 120°.

Explanation:

Given, (a+ b - c)(a + b + c) = 3ab

⇒ (a+ b)² - c² = 3ab

⇒ a² + b² - c² = ab

⇒ a² + b² - c² = `"2ab"/2`

⇒ `("a"^2 + "b"^2 - "c"^2)/"2ab" = 1/2`

⇒ cos C = `1/2`    ....[by cosine rule]

∴ C = 60°

⇒ A + B = 120°    ...[∵ A + B + C = 180°]