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In a Δ ABC, AD is the bisector of ∠ A, meeting side BC at D. If AC = 4.2 cm, DC = 6 cm, and BC = 10 cm, find AB.

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Given: Δ ABC and AD bisects ∠A, meeting side BC at D. And AC = 4.2 cm, DC = 6 cm, and BC = 10 cm. 

Required to find: AB

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

\(\frac{AB}{AC}\) = \(\frac{BD}{DC}\) 

\(\frac{AB}{4.2}\) = \(\frac{BD}{6}\) 

We know that, 

BD = BC – DC 

= 10 – 6 

= 4 cm 

\(\frac{AB}{4.2}\) = \(\frac{4}{6}\) 

AB = \(\frac{(2 \times 4.2)}{3}\)

∴ AB = 2.8 cm

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