Math CentralQuandaries & Queries


Question from Karlianna, a student:

find dimensions of a rectangle with least perimeter for given area
A) 30cm^2
b) 50cm^2


What is the shape of a rectangle with a given area that has the least perimeter? Is it tall and thin or short and fat or somewhere in between?

Let's try an example. Suppose that the area is 16 cm2.

dimensions perimeter
1 x 16 34
2 x 8 20
4 x 4 16
8 x 2 20
16 x 1 34



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