2018 · Q65
ABC is a triangle right angled at C with BC = a and AC = b. If p is the length of the perpendicular from C on AB, then which one of the following is correct?
Elementary MathematicsTrigonometry
- Aa²b² = p²(a² + b²)
- Ba²b² = p²(b² - a²)
- C2a²b² = p²(a² + b²)
- Da²b² = 2p²(a² + b²)
Explanation
Equating the two area formulas: (1/2)ab = (1/2)p√(a² + b²), so p = ab/√(a² + b²). Squaring gives p²(a² + b²) = a²b², option (A).