Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202523 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle with one of the angles 120^ , the lengths of the sides form an A.P. If length of the greatest side is 7 m , then the area of the triangle is

Options

  1. A15 3 4 ~m ^2
  2. B15 3 2 ~m ^2
  3. C15 2 ~m ^2
  4. D15 4 ~m ^2

Correct answer

A. 15 3 4 ~m ^2

Step-by-step solution

Let the triangle sides form an arithmetic progression, represented as x-d , x , and x+d , where x+d = 7 is the greatest side. The 120^ angle is opposite the longest side, designated as angle C . Applying the Law of Cosines: (x+d)^2 = (x-d)^2 + x^2 - 2(x-d)x 120^ Substituting 120^ = - 1 2 and x+d = 7 : 49 = (x-d)^2 + x^2 + x(x-d) 49 = 3x^2 - 3xd + d^2 Expressing d = 7 - x and substituting: 49 = 3x^2 - 3x(7-x) + (7-x)^2 49 = 7x^2 - 35x + 49 0 = 7x(x - 5) Sides must be positive, so x = 5 m, and d = 2 m. The sides are

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