Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In ABC , if A + C =4 ^2 B 2 , then the ratio between the perimeter of the triangle and (a+c) is

Options

  1. A2: 1
  2. B3: 2
  3. C5: 3
  4. D4: 1

Correct answer

B. 3: 2

Step-by-step solution

Given A+ C=4 ^2 B 2 aligned & 2 ( A+C 2 )+ ( A-C 2 )=4 ^2 B 2 & ( A-C 2 )=2 B 2 & A 2 C 2 + A 2 C 2 =2 B 2 & s(s-a) b c s(s-c) a b + (s-b)(s-c) b c (s-a)(s-b) a b & =2 (s-a)(s-c) a c & s b + s-b b =2 & a+c=2 b aligned Now, a+b+c a+c = 2 b+b 2 b = 3 2 =3: 2

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