Perimeter & Area: Which Structure Has Largest/Smallest?

[paul.redgate]

I had a question on a test & could not get an answer and was wondering if someone might have a clue. The question presented four buildings--a square, rectangle, L-shaped building and circle. All of the buildings are one-story and have the same area. The question was which structure had the largest perimeter & which had the smallest perimeter. None of the multiple choice answers were none of the above or all of the above. Any help would be greatly appreciated.

 

[berkeman]

I had a question on a test & could not get an answer and was wondering if someone might have a clue. The question presented four buildings--a square, rectangle, L-shaped building and circle. All of the buildings are one-story and have the same area. The question was which structure had the largest perimeter & which had the smallest perimeter. None of the multiple choice answers were none of the above or all of the above. Any help would be greatly appreciated.

What are the relevant equations? What is the area of a circle in terms of its diameter? In terms of its perimeter? What is the area of a square in terms of its perimeter (or more to the point, its perimeter in terms of its area)? Same question for a rectangle -- is a rectangle's perimeter bigger or smaller than a square with the same area?