Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2017MathematicsProperties of Triangles

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

Options

  1. A50
  2. B10 2
  3. C25
  4. D25 2

Correct answer

C. 25

Step-by-step solution

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

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All MHT CET PYQs