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.