ABC is a triangle right-angled at B with sides BC = a, CA = b and AB = c. Let p be the length of the perpendicular from B to AC. Which of the following statements is/are correct ? I. p = \frac{ac}{\sqrt{a^2 + c^2}} II. pb = ac Select the answer using the code given below :
- A. I only
- B. II only
- C. Both I and II ✓
- D. Neither I nor II
Correct Answer: C. Both I and II
Explanation
Area of the right triangle is \frac{1}{2}ac = \frac{1}{2}bp, so ac = pb (II is correct). Since hypotenuse b = \sqrt{a^2+c^2}, substituting this into p = \frac{ac}{b} gives p = \frac{ac}{\sqrt{a^2+c^2}} (I is also correct).
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