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
A. a2 + b2
B. $$\frac{1}{{{{\text{a}}^2}}} + \frac{1}{{{{\text{b}}^2}}}$$
C. $$\frac{{{{\text{a}}^2}{{\text{b}}^2}}}{{{{\text{a}}^2} + {{\text{b}}^2}}}$$
D. a2 - b2
Answer: Option C
Solution (By Examveda Team)
Length of perpendicular drawn from the right angle to hypotenuse,
$$\eqalign{ & {\text{P}} = \frac{{{\text{a}} \times {\text{b}}}}{{\text{H}}} \cr & {{\text{P}}^2} = \frac{{{{\text{a}}^2}{{\text{b}}^2}}}{{{{\text{H}}^2}}} \cr & {{\text{P}}^2} = \frac{{{{\text{a}}^2}{{\text{b}}^2}}}{{{{\text{a}}^2} + {{\text{b}}^2}}}\,\,\,\,\left[ {\because {{\text{H}}^2} = {{\text{a}}^2} + {{\text{b}}^2}} \right] \cr} $$
This Question Belongs to Arithmetic Ability >> Mensuration 2D
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