# Question #3b1bd

##### 1 Answer

Let's start from an inequality that states that *arithmetic average* of two non-negative numbers *geometric average* of these numbers

A short proof starts with an obvious inequality:

Therefore

or

or

or

Notice that equality is true only if

Let's apply this to our problem. Let

Then its perimeter is

The perimeter is, actually the length of a fencing and equals to 1200 meters. Therefore,

The problem asks about the "largest" field (in terms of the area). From the inequality above,

So, the largest possible area is 90000 only if

From

The largest possible field is 300x300. Its area is 90000.