Find the dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)

The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are 41.6, 41.6

The area is given as:

Let the dimension be x and y.

So, we have:

Make x the subject

The perimeter is calculated as:

Substitute

Expand

Differentiate

Set to 0

Rewrite as:

Divide both sides by -1

Multiply y^2

Divide by 2

Take square roots of both sides

Substitute in

Hence, the dimensions that minimize the perimeter are 41.6, 41.6

Read more about perimeters at:

link

Given :

Area of rectangle.

To Find :

The dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible.

Solution :

Let, the dimensions of rectangle is x and y.

Area, A = xy.

x = A/y.              ....1)

Perimeter, P = 2( x + y )

Putting value of x in above equation, we get :

For minimum P,

SO, it is a square.

Therefore, the dimensions are .24\sqrt{3}

Hence, this is the required solution.