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