Question

In a triangle ABC, AD is the bisector of angle A. If AC = 4.2 cm, DC = 6 cm, BC = 10 cm, then find AB?

• A. 3.4 cm
• B. 2.9 cm
• C. 2.7 cm
• D. 3 cm
• E. 2.8 cm

Hint:

Angle Bisector Theorem: \(\frac{AB}{AC} = \frac{BD}{DC}\).

Answer 1

Answer: (E)

Step 1: Using Angle Bisector Theorem:
The angle bisector divides the opposite side in the ratio of the adjacent sides.
\[ \frac{AB}{AC} = \frac{BD}{DC} \]
Given: AC = 4.2 cm, DC = 6 cm, BC = 10 cm.
So, BD = BC - DC = \(10 - 6 = 4\) cm.

Step 2: Applying the Theorem:
\[ \frac{AB}{4.2} = \frac{4}{6} \]
\[ AB = 4.2 \times \frac{4}{6} = 4.2 \times \frac{2}{3} = 1.4 \times 2 = 2.8 \text{ cm} \]