Question

Find the area of square maximum which is inscrived in a right angle trianfle

Answer 1

Consider - a,b as right legs and c as the hypotenuse.

Let side of square = s AC = b, BC = a, AB = c.

Right Angled Triangle

FB = as/b and AE = bs/a as the colored triangles are similar to the bigger triangle.

Steps to calculate area (S^2) :

1)Calculate GB and AD using right angle triangle rule for triangles GBF and ADE.

2)Calculate GD using right angle triangle rule for triangle GCD.

3)GD^2 = s^2. You get a quadratic equation in s which can be factorized. You get s = (abc)/(a^2 + b^2 +a.b)

If still not clarified will post the answer then.