Question

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^2


By writing suitable inequalities, find the possible values of x

Answer 1

Possible values of x are 50 < x < 110.

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.