In \(\triangle ABC\), \(AD\) is the bisector of \(\angle A\) meeting \(BC\) at \(D\). If \(AB = 30\) cm, \(BC = 20\) cm and the length of \(BD\) is 4 cm less than \(DC\), then the length (in cm) of…
Question and options
In , is the bisector of meeting at . If cm, cm and the length of is 4 cm less than , then the length (in cm) of is
- 45
- 28
- 36
- 48
Answer and explanation
Correct answer: A - 45
BD + DC = 20 and DC - BD = 4 give BD = 8, DC = 12. Angle bisector theorem: AB/AC = BD/DC, so 30/AC = 8/12 and AC = 45.
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