answer :

The border is 1 metre wide

The complete question is:

A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden.Find the width of the border.

Given:

Length of the garden= 6 m

Width of the garden =4 m

To find:

Find the width of the border.

Solution:

Area of the garden (Ag) = 6*4 = 24 m^2

Let the width of the border be x m

Area of the total garden along with the border (At) = (6+2x) (4+2x)

Area of the border = At - Ag

= (6+2x) (4+2x) - 24

Since area of border us same as area of garden:

(6+2x) (4+2x) - 24 = 24

(6+2x) (4+2x) = 48

24+ 20x + 4x^2 = 48

By factorizing method:

Since length cannot be negative, therefore x= 1 m

Therefore, the width of the border is 1 m.