In a triangle ABC, AB = 18 \text{ cm}, BC = 22 \text{ cm} and AC = 15 \text{ cm}. The bisector of \angle BAC intersects BC at D. What is (BD \times DC) equal to ?
- A. 121 \text{ cm}^2
- B. 120 \text{ cm}^2 ✓
- C. 117 \text{ cm}^2
- D. 96 \text{ cm}^2
Correct Answer: B. 120 \text{ cm}^2
Explanation
By the angle bisector theorem, \frac{BD}{DC} = \frac{AB}{AC} = \frac{18}{15} = \frac{6}{5}. Since BD + DC = 22, we divide 22 in a 6:5 ratio, giving BD = 12 and DC = 10. Thus, BD \times DC = 12 \times 10 = 120 \text{ cm}^2.
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