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KVPY2019MathematicsProperties of Triangles

The sides a ,   b ,   c of a triangle satisfy the relations c 2 = 2 a b and a 2 + c 2 = 3 b 2 . Then the measure of ∠ B A C , in degrees, is

Options

  1. A30
  2. B45
  3. C60
  4. D90

Correct answer

B. 45

Step-by-step solution

It is given that the sides of triangle, a , b and c satisfy the following relations c 2 = 2 a b and a 2 + c 2 = 3 b 2 From Eqs. (i) and (ii), we get a 2 + 2 a b = 3 b 2 ⇒ a 2 + 2 a b + b 2 = 4 b 2 ⇒ ( a + b ) 2 = ( 2 b ) 2 = ( b + b ) 2 ⇒ a = b , 80 c = 2 a

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