## Book: RS Aggarwal - Mathematics

#### Subject: Maths - Class 10th

##### Q. No. 60 of Exercise 10E

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60
##### 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.

Let the breadth of hall be x m

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

According to the question;

Area = 238cm2

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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