The perimeter of a rectangular plot is 130 m and its area is 1000 m². Take the length of the plot as x metres. Use the perimeter to write the value of breadth in terms of x. Use the values of length, breadth and area to write an equation in x. Solve the equation and calculate the length and breadth of the plot.

Given,

Perimeter = 130 m

Area = 1000 m²

Length = x meters

Let breadth = b meters

Perimeter = 2(length + breadth)

⇒ 130 = 2(x + b)

⇒ x + b = 65

⇒ b = 65 - x

Area = length × breadth

⇒ 1000 = x × (65 - x)

⇒ 1000 = 65x - x²

⇒ x² - 65x + 1000 = 0

⇒ x² - 40x - 25x + 1000 = 0

⇒ x(x - 40) - 25(x - 40) = 0

⇒ (x - 40) (x - 25) = 0

⇒ x = 40 or x = 25

If x = 40 then,

Length = x = 40 m

Breadth = 65 - x = 65 - 40 = 25 m

If x = 25 then,

Length = x = 25 m

Breadth = 65 - x = 65 - 25 = 40 m

Generally we consider length > breadth

Hence, length = 40 m and breadth = 25 m.