Answer :

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

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