Question

You have 60 meters of fencing and want enclose an area for a garden; however, you want to set up the fence so that the largest possible area is enclosed within the fence. The shape may be a rectangle or a square. What is the length and width of the shape that will given the maximum area?

Answer 1

The length and width of the shape that will give the maximum area is 15 meters by 15 meters

Explanation:

Mathematically, to maximize the area of a rectangle, the shape must be a square

what we are saying is that a square is the greatest rectangle

In that case , the length and width of the rectangle must be the same

Let’s have the width as w and since it is equal to length, we have the length too as w

We are given the length of the fencing which is the perimeter

Mathematically, the formula for this is ; 4w

Thus;

4w = 60

w = 60/4

w = 15 meters