# What is the smallest perimeter possible for a rectangle of area 16 in^2?

##### 1 Answer

The minimum perimeter is

#### Explanation:

If we denote one side of the rectangle with

so we can write, that

Now we can write perimeter

We are looking for the smallest perimeter, so we have to calculate derivative:

The extreme values can only be found in points where

Since, length is a scalar quantity, therefore, it cannot be negative,

When

You may be thinking, since both sides are of equal lengths, does it not become a square instead of a rectangle?

The answer is no because the properties of a rectangle are as follows:

- opposite sides are parallel
- opposite sides are congruent
- diagonals bisect each other
- diagonals are congruent
- each of the interior angles must be
#90^@#

Since there is no rule that states a rectangle cannot have all sides of equal length, all squares are rectangles, but not rectangles are squares.

Hence, the minimum perimeter is

P.S. What is a comedian's favourite square? a PUNnett square.