Question

In a Δ ABC, AD is the bisector of ∠A, meeting side BC at D. If BD = 2.5 cm, AB = 5 cm, and AC = 4.2 cm, find DC.

• A. 3.2 cm
• B. 2.5 cm
• C. 5 cm
• D. 2.1 cm

Answer 1

The correct option is D 2.1 cm

Since,
AD is the bisector of ∠A meeting side BC at D in Δ ABC
Hence, Δ ABD ~ Δ ACD

Now,
⇒$\frac{AB}{AC}=\frac{BD}{CD}$

⇒$\frac{5}{4.2}=\frac{2.5}{CD}$

⇒$5\times CD=2.5\times 4.2$

⇒$CD=2.1cm$

$\therefore$ DC = 2.1 cm.