# Question #ef706

##### 2 Answers

The optimal Area to Perimeter ratio is achieved by a circle.

Removal of any part of the circle's perimeter (circumference) to construct any other shape is counter productive.

Use the entire 36 meters for the circle (make your square

This minimization problem turns into a minimization on a closed interval. I haven't found a general post on the closed interval method. (Maybe the link owl will spot one.)

Let

Then the sides of the square are each of length

The piece formed into a circle measures

For a circle,

The total area will be

Minimize the function of the interval:

The zero of

The critical numbers are

Calculate the Total area for the 3 values of