Let the breadth of the rectangle be x m

Thus the length of the rectangle is (x + 8) m

Area of the field is 240 m² = length . breadth

x(x + 8) = 240

x² + 8x - 240 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = 8 c = - 240

= 1. - 240 = - 240

And either of their sum or difference = b

= 8

Thus the two terms are 20 and - 12

Difference = 20 - 12 = 8

Product = 20. - 12 = - 240

x² + 20x - 12x - 240 = 0

x(x + 20) - 12(x + 20) = 0

(x + 20) (x - 12) = 0

x = 12 or x = - 20 (but breadth cannot be negative)

The breadth of the rectangle = 12m