If `A` be the area of a right triangle and `b` one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is `(2A B)/(sqrt(b^4+4A^2))`

Explanation

To prove that the length of the altitude on the hypotenuse of a right triangle is given by the formula \(\frac{2AB}{\sqrt{b^4 + 4A^2}}\), where \(A\) is the area of the triangle and \(b\) is one of the sides containing the right angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Right Triangle**:
Let triangle \(ABC\) be a right triangle with the right angle at \(B\). Let \(AB = c\), \(BC = b\), and \(AC = a\). The area \(A\) of triangle \(ABC\) can be expressed as:
\[
A = \frac{1}{2} \times AB \times BC = \frac{1}{2} \times c \times b
...