Question

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.​

Answer 1

answer :

The border is 1 metre wide

Answer 2

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

$4 {x}^{2} + 20x - 24 = 0$

${x}^{2} + 5x - 6 = 0$

By factorizing method:

${x}^{2} + 6x - x - 6 = 0$

$x(x + 6) - 1(x + 6) = 0$

$(x + 6)(x - 1) = 0$

$x = - 6 \: and \: 1$

Since length cannot be negative, therefore x= 1 m

Therefore, the width of the border is 1 m.