What is the smallest perimeter possible for a rectangle of area 16 in^2?
The minimum perimeter is
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,
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
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.