Answer:
Smallest possible perimeter 16 inches.
Length : 4 inches,
Width : 4 inches.
Step-by-step explanation:
Let x represent length and y represent width of rectangle.
We have been given that area of a rectangle is 16 square inches.
We know that area of rectangle is product of its length and width. We can represent our given information in an equation as:
We know that perimeter of rectangle is sum of its all sides that is:
From equation (1), we will get:
Upon substituting this value in equation (2), we will get:
Now, we will find the derivative of perimeter equation as:
Now, we will equate our derivative equal to 0 to find critical points as:
Take square root of both sides:
Since length cannot be negative, therefore, .
Now, we will find 2nd derivative as:
We know that where 2nd derivative is positive, the point is a minimum. Let us substitute in 2nd derivative.
Since , therefore is a minimum.
Let us solve for y using equation as:
Therefore, width and length of 4 inches each will result in smallest perimeter.
Therefore, the smallest possible perimeter would be 16 inches.