A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m2. Find the width of the path.
Let the width of the path be x m
Length of the field including the path = 16 + x + x = 16 + 2x
Breadth of the field including the path = 10 + x + x = 10 + 2x
Area of field including the path – Area of field excluding the path = Area of path
(16 + 2x) (10 + 2x) – (16.10) = 120
160 + 32x + 20x + 4x2 – 160 = 120
4x2 + 52x – 120 = 0
x2 + 13x – 30 = 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 = 13 c = – 30
= 1. – 30 = – 30
And either of their sum or difference = b
= 13
Thus the two terms are 15 and – 2
Difference = 15 – 2 = 13
Product = 15. – 2 = – 30
x2 + 15x – 2x – 30 = 0
x(x + 15) – 2(x + 15) = 0
(x + 15) (x – 2) = 0
x = 2 or x = – 15
x = 2 (width cannot be negative)
Thus the width of the path is 2 m