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

Question

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, 17 2, 15 2, 17 4, 15 4

MARKS App · Accepted Answer

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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