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
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