Question
The bisector of ∠ B in ∆ ABC meets AC at D. If AB =
12 cm, BC = 18 cm and AC = 15 cm, then the length of AD (in cm) is:Solution
Given, AB = 12 cm, BC = 18 cm and AC = 15 cm In ΔABC, BD bisector of ∠B, then AB/BC = AD/DC ⇒ 12/18 = AD/DC ⇒ AD ∶ DC = 12x ∶ 18x ⇒ AC = AD + DC = 15 cm ⇒ 12x + 18x = 15 ⇒ 30x = 15 ⇒ x = 15/30 ⇒ x = 1/2 ⇒ AD = 12 × (1/2) ⇒ AD = 6 cm
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