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A square.
A 9 x 1 rectangle has a perimeter of 20 and an area of 9; A 9.5 x 0.5 rectangle has the same perimeter but an area of 4.75; You can go a long way along this road...
Yes, there is. The area of a rectangle sets a lower limit on its perimeter.If the area is A, then the quadrilateral shape with the smallest perimeter has sides of length sqrt(A). Therefore the minimum perimeter is 4*sqrt(A). The perimeter can have any value grater than that since the area of the rectangle can be maintained while making it thinner and longer and thus increasing its perimeter with out any upper limit.
I think this means we have a shape with a perimeter 39cm and we are asked what is the smallest area. It is a rectangle of length 19.5cm and width zero. Or perhaps it should read area 49 cm squared., what is the smallest periimeter. A circle with 49=pi x r2. Then perimeter=pi x 2r
For any given area, the rectangle closest to a square will have the smallest perimeter; and the one that is most "stretched out" has the largest perimeter. In this case, that would be a width of 1 and a length of 2014.