In Δ A B C if sin 2 ⁡ A + sin 2 ⁡ B = sin 2 ⁡ C and l A B = 10 , then the maximum value of the area of Δ A B C is

Question

In Δ A B C if sin 2 ⁡ A + sin 2 ⁡ B = sin 2 ⁡ C and l A B = 10 , then the maximum value of the area of Δ A B C is, 50, 10 2, 25, 25 2

MARKS App · Accepted Answer

sin 2 ⁡ A + sin 2 ⁡ B = sin 2 ⁡ C ⇒ a 2 + b 2 = c 2 (Sine Rule) ⇒ Right Angled ∆ ⇒ C = 90 o , B = 90 o − A Also Area A Δ A B C = 1 2 a b ..........(i) = 1 2 ( c sin A ) ( c cos A ) = 50 sin A cos A = 25 sin A ≤ 25 So maximum value of Δ A B C = 25

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