Question 695553
Lenghth=a

width=b

perimeter = 2(a+b)= 800

a+b=400

now Area= a x b, which can be infinite combinations from (1,399), (2,398),(3,397) etc.. upto (399,1). 

multiply certain values and see the result.

product of the sides increases gradually and starts decreasing after halfway.

So the product is maximum when a and b are both 400.

Or

When the rectangle of given perimeter is a square, it will have maximum area