Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202421 May 2024Evening ShiftMathematicsProperties of TrianglesActual

If 7 and 8 are the lengths of two sides of a triangle and ' a ' is the length of its smallest side. The angles of the triangle are in AP and ' a ' has two values a₁ and a₂ satisfying this condition. If a₁ a₂ then 2 a₁+3 a₂=

Options

  1. A15
  2. B21
  3. C24
  4. D28

Correct answer

B. 21

Step-by-step solution

Let angles be A, 180^ -3 A, 2 A Then 2 (180^ -3 A )=A+2 A A=40 Angles are 40^ , 60^ , 80^ Now, b^2=c^2+a^2-2 a c 60^ 49=64+a^2-8 a aligned & a^2-8 a+15=0 a=3,5 & a₁=3, a₂=5 2 a₁+3 a₂=21 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