The perimeter of a rectangular plot is 180 m and its area is 1800 sq.metre. Take the length of the plot as x m. Use the perimeter to write the value of the breadth in terms of x. Use the value of length , breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.

The correct answer is: ∴ Length & Breadth of the given rectangle are 60 m & 30 m, respectively

Step-by-step solution:-
As given in the sum,
Let the length of the given rectangle be x m
Length = x m ....................................................................................... (Equation i)
We know that-
Perimeter of a rectangle = 2 (length + breadth)
∴   Perimeter of a rectangle = 2 (x + breadth) ........................................... (From Equation i)
∴  180 = 2 (x + breadth) ........................................... (From given information)
∴  180 / 2 = x + breadth
∴  90 = x + breadth
∴  90 - x = breadth .................................................... (Equation ii)
Area of a rectangle = length × breadth
∴   Area of a rectangle = x × (90 - x) ........................................................ (From Equations i & ii)
∴  1,800 = 90x - x² ........................................................... (From given information)
∴   x² - 90x + 1,800 = 0
Comparing this quadratic equation with the general form, i.e. ax2 + bx + c = 0, we get-
 a = 1, b = -90, c = 1,800
We can solve the above quadratic equation using factorization method as follows-
Steps for Factorization method-
Step-1: a × c = 1 × 1,800 = 1,800
Step-2: Factorize 1,800 in such a way that the 2 factors, when added, gives the value b = -90
i.e. 1,800 = -30 × -60
& -30 + (-60) = -90 = b
∴  x² - 90x + 1,800 = 0
∴  x² - 60x - 30x + 1,800 = 0
∴  x (x - 60) - 30 (x - 60) = 0
∴  (x - 30) (x - 60) = 0
either x - 30 = 0 or x - 60 = 0
either x = 30 or x = 60
From Equations i & ii-
When Length = x = 30
Breadth = 90 - x = 90 - 30 = 60
When Length = 60
Breadth = 90 - x = 90 - 60 = 30
Since Length of a rectangle should be greater than its breadth,
Length = 60 & Breadth = 30
Final Answer:-
∴ Length & Breadth of the given rectangle are 60 m & 30 m, respectively.