if the sum of lengths of hypotenuse and a side of right triangle are given, prove the area of the triangle is maximum when angle between them is pi/3

area of the triangle is half the product of base and height...

name the unknown side as x

convert the known value into hypotenuse and unknown sides by using pythagoras theorem

differentiate and equal it to zero..

you would get the value of x

the find the angle between the sides