Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202018 Sep 2020Morning ShiftMathematicsProperties of TrianglesActual

In triangle (A B C, A 2 = B 3 = C 4 ), then the value of ( ^2 A+ ^2 B+ ^2 C= )

Options

  1. A( 101 8 )
  2. B( 111 8 )
  3. C( 121 8 )
  4. D( 91 8 )

Correct answer

B. ( 111 8 )

Step-by-step solution

In a ( A B C ), it is given that ( A 2 = B 3 = C 4 =k (Let) ) ( A=2 k, B=3 k ) and ( c=4 k ). Since in ( A B C ), ( aligned & A+ B+ C= A B C & 9 k=24 k^3 k^2= 3 8 k 0 & Now, ^2 A+ ^2 B+ ^2 C & =3+ ^2 A+ ^2 B+ ^2 C & =3+k^2[4+9+16]=3+ 3 8 (29)= 24+87 8 = 111 8 . 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