In a ΔABC right angled at B, D is a point on AC such that BD is an angle bisector of B. If AD = 12 cm, CD = 16 cm then find the perimeter of triangle ABC.

  1. 49.6 cm
  2. 67.2 cm
  3. 56.4 cm 
  4. 48 cm

Answer (Detailed Solution Below)

Option 2 : 67.2 cm
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Detailed Solution

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Given

AD = 12 cm, CD = 16 cm 

Formula used 

Angle Bisector theorem,

AD/CD = AB/BC

Perimeter of triangle = Sum of all sides

Calculation

F1 Ashish Shraddha 06.08.2021 D2 1

In Δ ABC, BD is an angle bisector of ∠B

AD/CD = AB/BC

⇒ 12/16 = AB/BC

⇒ AB : BC = 3 : 4

From the triplets of right angle triangle

If AB = 3x and BC = 4x

then AC = 5x

AC = 12 + 16 = 28 cm

⇒ 5x = 28 cm

⇒ x = 5.6 cm

Perimeter of triangle = 5x + 3x + 4x = 12x

⇒ 67.2 cm

∴ The required answer is 67.2 cm

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