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

Let length of rectangle be x meters.

Given,

Perimeter = 180 m

∴ 2(l + b) = 180

⇒ 2(x + b) = 180

⇒ x + b = 90

⇒ b = (90 - x) m.

Area = l × b

∴ x(90 - x) = 1800

⇒ 90x - x² = 1800

⇒ x² - 90x + 1800 = 0

⇒ x² - 60x - 30x + 1800 = 0

⇒ x(x - 60) - 30(x - 60) = 0

⇒ (x - 30)(x - 60) = 0

⇒ x - 30 = 0 or x - 60 = 0

⇒ x = 30 or x = 60.

If x = 30, 90 - x = 60 and x = 60, 90 - x = 30.

Hence, breadth = (90 - x) m, equation : x(90 - x) = 1800 and length of rectangle = 60 m and breadth = 30 m.