a and b are two sides adjacent to the right angle of a right angled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex. Then p2 is equal to

Answer: Option C

Solution

Answer: Option C

Solution:

Length of perpendicular drawn from the right angle to hypotenuse,
$$\begin{array}{rl}& \text{P}=\frac{\text{a}\times \text{b}}{\text{H}}\\ & {\text{P}}^2=\frac{{\text{a}}^2{\text{b}}^2}{{\text{H}}^2}\\ & {\text{P}}^2=\frac{{\text{a}}^2{\text{b}}^2}{{\text{a}}^2+{\text{b}}^2}\left[\because {\text{H}}^2={\text{a}}^2+{\text{b}}^2\right]\end{array}$$