A landscape designer has to design a rectangular pad of concrete at the centre of a rock garden. The length must be less than or equal to twice the width; the perimeter must be less than or equal to 40 m; and the area must be greater than or equal to 60 m^2.

1.)Write as system of inequalities to represent the constraints in this problem situation.

x=width y=length
y<=2x
2(x+y)<=40
xy>=60

your inequalities are right. :)

To represent the given constraints as a system of inequalities, we can use the following equations:

1) Length must be less than or equal to twice the width:
y ≤ 2x

2) Perimeter must be less than or equal to 40 m:
2(x + y) ≤ 40

3) Area must be greater than or equal to 60 m²:
xy ≥ 60

In these equations, 'x' represents the width and 'y' represents the length of the rectangular pad of concrete.