Let the length and breadth of rectangular plot be x and y respectively.

Area = xy = 180 sq m – – – – – (1)

2(x + y) –x = 39

2x + 2y – x = 39

2y + x = 39

x = 39 – 2y

Putting the value of x in (1) we get

(39 – 2y)y = 180

39y – 2y² = 180

2y² – 39y + 180 = 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 = 2 b = – 39 c = 180

= 2.180 = 360

And either of their sum or difference = b

= – 39

Thus the two terms are – 24 and – 15

Difference = – 24 – 15 = – 39

Product = – 24. – 15 = 360

2y² – 24y – 15y + 180 = 0

2y(y – 12) – 15(y – 12) = 0

(y – 12)(2y – 15) = 0

y = 12 or y = 15/2 = 7.5

if y = 12 x = 39 – 2y = 39 – (2.12) = 39 – 24 = 15

if y = 7.5 x = 39 – 2y = 39 – [(2)(7.5)] = 39 – 15 = 24

Hence either l = 24 m, b = 7.5 m or l = 15 m, b = 12 m