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Home » In ∆ABC, it is given that AD is the internal bisector of ∠A. If BD = 4cm, DC = 5cm and AB = 6cm, then AC = ? (a) 4.5cm (b) 8cm (c) 9cm (d) 7.5cm
In ∆ABC, it is given that AD is the internal bisector of ∠A. If BD = 4cm, DC = 5cm and AB = 6cm, then AC = ? (a) 4.5cm (b) 8cm (c) 9cm (d) 7.5cm
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
In ∆ABC, it is given that AD is the internal bisector of ∠A. If BD = 4cm, DC = 5cm and AB = 6cm, then AC = ? (a) 4.5cm (b) 8cm (c) 9cm (d) 7.5cm

Correct Answer: (d) 7.5 cm

Explanation:

 

 

 

Given,

AD bisects angle A

Applying angle bisector theorem,

\begin{array}{l} \frac{{BD}}{{DC}} = \frac{{AB}}{{AC}}\\ \frac{4}{5} = \frac{6}{x}\\ x = \frac{{5 \times 6}}{4}\\ x = 7.5\\ \therefore AC = 7.5cm \end{array}

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