What is the smallest perimeter possible for a rectangle whose area is 16 in^2, and what are its dimensions?

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.

the first question mark is 6 and the second question mark is 26 (the square root)

step-by-step explanation: