Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2014MathematicsProperties of Triangles

In any A B C, (a+b+c)(b+c-a)(c+a-b)(a+b-c) 4 b^2 c^2 equals to

Options

  1. A^2 B
  2. B^2 A
  3. C^2 B
  4. D^2 A

Correct answer

D. ^2 A

Step-by-step solution

aligned & (a+b+c)(b+c-a)(c+a-b)(a+b-c) 4 b^2 c^2 & = 2 s(2 s-2 a)(2 s-2 b)(2 s-2 c) 4 b^2 c^2 & = 16[s(s-a)(s-b)(s-c)] 4 b^2 c^2 ( a+b+c=2 s) & = 4 ^2 b^2 c^2 = ( 2 b c )^2= ^2 A [ A= 2 b c ] aligned

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 AP EAMCET PYQs