Question

The length and the breadth of a rectangular plot, in meters, are x and y such that x + y = 100 and x - y = 20. The area of the plot in sq. meters is ________.

Answer 1

Given :

• Length of plot (L) = x m
• Breadth of plot (B) = y m

To Find :

• Area of the rectangular plot in m²

Solution :

We're given two equations, from which we've to calculate the value of length and breadth.

⇒x + y = 100 ........(1)

⇒x - y = 20 .........(2)

(1) + (2)

⇒(x + y) + (x - y) = 100 + 20

⇒x + x + y - y = 120

⇒2x + 0 = 120

⇒2x = 120

⇒x = 120/2

⇒x = 60

$\therefore$ Length of plot is 60 m

______________________

Put value of x in (1)

⇒x + y = 100

⇒60 + y = 100

⇒y = 100 - 60

⇒y = 40

$\therefore$ Breadth of plot is 40 m

_________________________________

Now, area of plot

⇒Area = length * breadth

⇒Area = 40 * 60

⇒Area = 2400

$\therefore$ Area of rectangular plot is 2400 m²