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

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