How can you find the perimeter of a rectangle if you only know the area of it? The area of a rectangle 756 units squared. What is its perimeter?

1 Answer
Alan P.
Dec 21, 2015

It is not possible to determine the perimeter of a figure given its area.
(It is however possible to determine it's minimum perimeter; in this case #4sqrt(756)~=109.98#)

Explanation:

The diagram below shows how the area dose not determine the perimeter (notice that for ease of demonstration I've used a different area than given in the question.

enter image source here

The perimeter is minimized if the rectangle is a square (hinted at but not proven by the above diagram).

In this case for the question data value (area#=756#)
each side would have a length of #sqrt(756)#
and the perimeter would be #p=4sqrt(756)#

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