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KVPY2020MathematicsProperties of Triangles

In a triangle A B C , the angle bisector B D of ∠ B intersects A C in D . Suppose B C = 2 ,   C D = 1 and B D = 3 2 . The perimeter of the triangle A B C is

Options

  1. A17 2
  2. B15 2
  3. C17 4
  4. D15 4

Correct answer

B. 15 2

Step-by-step solution

2 a c a + c cos B 2 = 3 2 ⇒ 4 c 2 + c 4 + 9 2 - 1 2 × 2 × 3 2 = 3 2 ⇒ c = 3 Now, c a = A D D C ⇒ A D = 3 2 ⇒ b = 5 2 ⇒ Perimeter = 15 2

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