Q. 655.0( 3 Votes )

A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.

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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