Q. 603.8( 6 Votes )

The length of a hall is 3 meters more than its breadth. If the area of the hall is 238 sq metres, calculate its length and breadth.

Answer :

Let the breadth of hall be x m

The length of hall will be (x + 3) m


According to the question;


Area = 238cm2


Area = length .breadth


x2 + 3x – 238 = 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 = 3 c = – 238


= 1. – 238 = – 238


And either of their sum or difference = b


= 3


Thus the two terms are 17 and – 14


Difference = 17 – 14 = 3


Product = 17. – 14 = – 238


x2 + 17x – 14x – 238 = 0


x(x + 17) – 14(x + 17) = 0


(x + 17) (x – 14) = 0


x = – 17 or x = 14


x = 14 ( x cannot be negative)


Hence the breadth of hall is 14 m and the length of hall is (14 + 3) = 17m


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