'x' and 'y' are two adjacent side of the right angle of a right angled triangle and 'a' is the perpendicular draw to the hypotenuse from the opposite vertex. Then a² is equal to?

\(\frac{x^2y^2}{x^2+y^2}\)

Area of triangle,

\(\frac{1}{2}×x×y\)=\(\frac{1}{2}×a×\sqrt {x^2+y^2}\)

squaring both side

x²y² = a²(x² + y²)

\(a^2 =\frac{x^2y^2}{x^2+y^2}\)