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KVPY2018MathematicsProperties of Triangles

Let P   Q   R be a triangle is which P   Q = 3 . From the vertex R , draw the altitude R   S to meet P   Q at S . Assume that R S = 3 and P   S = Q   R . Then, P   R equals

Options

  1. A5
  2. B6
  3. C7
  4. D8

Correct answer

C. 7

Step-by-step solution

Given, in Δ P Q R P Q = 3 Altitude R S = 3 ⇒ P S = Q R In Δ S Q R , Q R 2 = S R 2 + S Q 2 P S 2 = ( 3 ) 2 + ( Q P - P S ) 2 [ ∵ S Q = P Q - P S ] P S 2 = 3 + ( 3 - P S ) 2 P S 2 = 3 + 9 - 6 P S + P S 2 ⇒ P S = 2 In Δ P R S , P R 2 = P S 2 + R S 2 = ( 2 ) 2 + ( 3 ) 2 = 4 + 3 P R = 7

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