If A be the area of a right triangle and b one of the sides containing the right angle, the length of the altitude on the hypotenuse is__________.

a) 2A/√(b^{2}+2A^{2}) b) 2Ab/ √(b^{4}+4A^{2}) c)2Ab^{2}/ √(b^{3}+4A^{2}) d)2A^{2}b/ √(b^{4}+3A^{2})

Let *A* be the area of the right triangle and *b *be one of the sides containing the right angle.

Let *x* be the length of the other leg

Let us observe the following figure.

Area of the triangle is

Thus,

Now apply Pythagorean Theorem.

Thus,

Area of the triangle ABC is

Hence (b) is the correct option.

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