Answer:
5x5 for a perimeter of 20
Explanation:
A couple of ways to think about this, one is knowing that a circle has the highest area-to-perimeter ratio, and a square is the closest rectangle to being a circle. this would mean a^2=25 4a=x a^sqrt(25) a=5.
The other way to go both extremes of a rectangle, a 25x1 rectangle, and a 5x5 rectangle are the furthest apart in terms of structure. a 25x1 rectangle has a perimeter of 52 while a 5x5 rectangle has a perimeter of 20. If you want to do a bunch of rectangles in between such as a 6x4.166, you get an area of 20.33. If you keep doing this you find that as you get closer to the same length sides, the area decreases. so you make it a square and
a^2=25 4a=x a^sqrt(25) a=5.