If the sum of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is π/3 .

If the sum of the hypotenuse and a side of a right angled triangle is given show that the area of the triangle is maximum when the angle between them is π/3 .

Let ABC be a right angled triangle in which side BC = x(say) and hypotenuse AC = y (say).,Given x+y = k(const.) ⇒ y = k - x,Now the area of the triangle ABC is given by  ,