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Any number you like that is greater than 33.63 metres (to 2 dp).

A circle of perimeter 33.63 m (radius 5.35 m approx) will enclose an area of 90m2. An ellipse (oval shape) with the same area will have a larger perimeter and the peimeter can be increased infinitely by making the shape flatter.

The smallest quadrilateral would be a square with sides of 9.49 metres (approx) giving a peimeter of 37.95 m.

The following rectangles will all have an area of 90 m2 but increasing perimeters (P):

9m*10m rectange: P = 38 metres.

0.9m*100m rectangle: P = 201.8 metres.

0.009*1000m: P = 2000.018 metres.

0.0009*10000m: P = 20000.0018 metres.

By now, you should see that there is nothing to limit the maximum value for the perimeter (except perhaps when the width of the rectangle reaches the Planck length!).

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14y ago

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