Question

The perimeter of a rectangular plot is 180 m and its area is 1800 m². Take the length of the plot as x m. 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.

Answer 1

The perimeter of a rectangular field = 180m
and area = 1800m²
Let length = xm
But length + breadth = `(180)/(2)` = 90m
∴ breadth = (90 - x)m
According to the condition,
x(90 - x) = 1800
⇒ 90x - x² - 1800 = 0
⇒ x² - 90x + 1800 = 0
⇒ x² - 60x - 30x + 1800 = 0
⇒ x(x - 60) - 30(x - 60) = 0
⇒ (x - 60)(x - 30) = 0
EIther x - 60 = 0,
then x = 60
or
x - 30 = 0,
then x = 30
∵ Length is greater than its breadth
∴ Length = 60m
and breadth = 90 - 60 = 30m.