The perimeter of a rectangular plot is 180 m and its area is 1800 m². Take the length of the plot as x meters. Use the perimeter 180 m to write the value of the breadth in terms of x . Use the values of length, breadth and the area to write an equation in x . Solve the equation to calculate the length and breadth of the plot.

Length of rectangular plot = x meters

Perimeter = 2(length + breadth)

$\Rightarrow 2(x + \text{Breadth}) = 180 \\[0.5em] \Rightarrow x + \text{Breadth} = 90 \\[0.5em] \Rightarrow \text{Breadth} = 90 - x$

Area of the rectangle = Length $\times$ Breadth

Given, Area of rectangle = 1800 m²

$\Rightarrow x(90 - x) = 1800 \\[0.5em] \Rightarrow 90x - x^2 = 1800 \\[0.5em] \Rightarrow x^2 - 90x + 1800 = 0 \\[0.5em] \Rightarrow x^2 - 30x - 60x + 1800 = 0 \\[0.5em] \Rightarrow x(x - 30) - 60(x - 30) = 0 \\[0.5em] \Rightarrow (x - 30)(x - 60) = 0 \\[0.5em] \Rightarrow x - 30 = 0 \text{ or } x - 60 = 0 \\[0.5em] \Rightarrow x = 30 \text{ or } x = 60$

Breadth = (90 - x) meters
Equation in x : x(90 - x) = 1800
Length of rectangle = 60 m , Breadth of rectangle = 30 m