Answer :

Let the length and breadth of rectangular plot be x and y respectively.

Area = xy = 180 sq m – – – – – (1)


2(x + y) –x = 39


2x + 2y – x = 39


2y + x = 39


x = 39 – 2y


Putting the value of x in (1) we get


(39 – 2y)y = 180


39y – 2y2 = 180


2y2 – 39y + 180 = 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 = 2 b = – 39 c = 180


= 2.180 = 360


And either of their sum or difference = b


= – 39


Thus the two terms are – 24 and – 15


Difference = – 24 – 15 = – 39


Product = – 24. – 15 = 360


2y2 – 24y – 15y + 180 = 0


2y(y – 12) – 15(y – 12) = 0


(y – 12)(2y – 15) = 0


y = 12 or y = 15/2 = 7.5


if y = 12 x = 39 – 2y = 39 – (2.12) = 39 – 24 = 15


if y = 7.5 x = 39 – 2y = 39 – [(2)(7.5)] = 39 – 15 = 24


Hence either l = 24 m, b = 7.5 m or l = 15 m, b = 12 m


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