a and b are two sides adjacent to the right angle vertex B of a right angle ΔABC and p is perpendicular drawn from the B on side AC. Then p2 is equal to:
Answer & explanation
Correct answer: option 1
Hypotenuse (AC) = \(\sqrt {AB^2 + BC^2}\) = \(\sqrt {a^2 + b^2}\)
Area of Δ ABC = \(\frac{1}{2}\) AB × BC or \(\frac{1}{2}\) AC × BD
⇒ \(\frac{1}{2}\) AB × BC = \(\frac{1}{2}\) AC × BD
⇒ AB × BC = AC × BD
⇒ ab = \(\sqrt {a^2 + b^2}\) × p
squaring both sides
⇒ a2 b2 = (a2 + b2) × p2
⇒ p2 = \(\frac{a^2 b^2}{a^2 + b^2}\)