Question

The maximum area of a triangle whose sides a, b, c satisfy

0 £ a £ 1, 1 £ b £ 2, 2 £ c £ 3

• A. 2
• B. 1
• C. 0.5
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

Let the vertices be O(0, 0), A(a, 0) and B(a₁, b₁) where a £ 1 and 1 £ $\alpha_{1}^{2}$+ $\beta_{1}^{2}$£ 4

Ž area of DOAB is maximum where a = 1 and (a₁, b₁) is

(2, 0)

In this case a = 1, b = 2 and c = $\sqrt{5}$which satisfies 2 £ c £ 3

Ž maximum area is 1.