[tzs]

Note that when a = b we have an equilateral triangle, with area a^2/2.

Draw a line from the 90 degree angle to side c, bisecting the 90 degree angle into two 45 degree angles. This divides the original triangle into two smaller triangles.

From the fact that the sum of the interior angles of a triangle is 180 degrees, it is not hard to see that the two smaller triangles are both equilateral, with sides of a, c/2, and c/2, and the angle between their two c/2 sides is 90 degrees.

That gives c^2/8 for the area of each of the smaller triangles, or c^2/4 for the area of the original triangle which we know to be a^2/2. So c^2/4 = a^2/2 or c^2 = 2 a^2 = a^ + a^2.

[ipince]

Ok, but those triangles aren't equilateral but isosceles :)