Hi,
For any given perimeter, generally equilateral polygon (a polygon with all sides equal) will have maximum area.
For example, for a given perimeter of a triangle equilateral triangle will have maximum area.
But, in the above question we have a right angle triangle, hence it can't be an equilateral triangle.
So, next best we can make an isosceles triangle.
Given: a+b = 40 for an isosceles right traingle a = b => 2a = 40 => a = 20 = b
Area of traingle= 1/2*a*b = 1/2*20*20 = 200 units.
Required answer is 200 units.
Hope this helps.
Thanks.