# How do you find the maximum area of a rectangle with perimeter of 40 ft?

##### 1 Answer

Feb 9, 2016

Your gut feeling may tell you it's a square, with sides 10 ft, or a total area of 100 sqft.

#### Explanation:

You can divert from this and see if the area gets any larger, or you can use the mathematical way:

If the length =

As for the area

And we have to find an extreme for that:

We can do this by setting the derivative to

Just as we thought in the first place.

graph{20x-x^2 [-131.6, 135.4, -8.4, 125.1]}