2026 · Q49
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?
- Ip = ac/√(a^2 + c^2)
- IIpb = ac Select the answer using the code given below:
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
The area is ac/2=bp/2, so p=ac/b; by Pythagoras b²=a²+c², hence p=ac/√(a²+c²) — I is correct — and pb=ac — II is correct. Both are correct, option C. The familiar 3-4-5 triangle is the special case: p=12/5=2.4, and indeed pb=12=ac.