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AP EAMCET2005MathematicsProperties of Triangles

Two sides of a triangle are given by the roots of the equation x^2-5 x+6=0 and the angle between the sides is 3 . Then, the perimeter of the triangle is

Options

  1. A5+ 2
  2. B5+ 3
  3. C5+ 5
  4. D5+ 7

Correct answer

D. 5+ 7

Step-by-step solution

Given equation is aligned x^2-5 x+6 & =0 (x-3)(x-2)=0 x & =3,2 aligned These are the sides of a triangle Let a=3, b=2, C= 3 aligned & C= a^2+b^2-c^2 2 a b & ( 3 )= 3^2+2^2-c^2 2 3 2 & 1 2 = 13-c^2 12 & c^2=13-6=7 & c= 7 & c= 7 (neglect - ve sign) & Perimeter of a triangle =a+b+c & =3+2+ 7 & =5+ 7 & aligned

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