In a triangle ABC, angle B=90^\circ and p is the length of the perpendicular from B to AC. If BC=10 cm and AC=12 cm, then what is the value of p?
- A. \frac{5\sqrt{11}}{3} ✓
- B. \frac{10\sqrt{11}}{3}
- C. \frac{40}{\sqrt{61}}
- D. \frac{12}{25}
Correct Answer: A. \frac{5\sqrt{11}}{3}
Explanation
By Pythagoras theorem, AB = \sqrt{AC^2 - BC^2} = \sqrt{144 - 100} = \sqrt{44} = 2\sqrt{11}. The area of the right triangle is \frac{1}{2} \times AB \times BC = \frac{1}{2} \times AC \times p. Equating them: 2\sqrt{11} \times 10 = 12 \times p \implies p = \frac{20\sqrt{11}}{12} = \frac{5\sqrt{11}}{3} cm.
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