Find the dimensions of a rectangle with a perimeter 108m whose area is as large as possible.

Solution:

It is given that

Perimeter of the rectangle = 108m

Area is as large as possible if both the values are the same number.

In order to have a maximum area in a rectangle, the dimensions should be equal.

Consider the dimensions as x

So perimeter can be written as

2 (x + x) = 108

2 (2x) = 108

By further calculation

4x = 108

Divide both sides by 4

x = 27

Therefore, the dimensions of a rectangle is 27m × 27m.

Find the dimensions of a rectangle with a perimeter 108m whose area is as large as possible.

Summary:

The dimensions of a rectangle with a perimeter 108m whose area is as large as possible is 27m × 27m.