# Maximization

A Farmer wants to construct a fence. The area that he is going to enclose is rectangular, but one of the sides is a river (assumed to be straight). If he has 120 m of fence, what is the maximum surface that he can enclose?

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#### Solution Preview

The rectangle is characterized by two numbers a and b (the lengths of the distinct sides). Suppose that the side by the river is of length a, hence the amount of fence that the farmer needs is:

a + b + b = 120 m.

The area enclosed by the rectangle is ...

#### Solution Summary

This shows how to maximize area given a perimeter.

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