The width of rectangular field is x metres. the length of the field is 30m longer than the width. the perimeter of the field is less than 500m. the area of the field is greater than 4000m^2by writing suitable inequalities, find the possible values of x

Possible values of x are   50 < x < 110.

Step-by-step explanation:

Consider the perimeter of the field:

2x + 2(x + 30) < 500

2x + 2x + 60 < 500

4x < 440

x < 110.

Consider the area of the field:

x(x + 30 ) > 4000

x^2 + 30x - 4000 > 0

(x - 50)(x + 80) > 0

The critical values are x = -80 and 50.

As x is a width it must be positive so x > 50.

the least common denominator is 40

this answer is !