# The perimeter of a rectangular plot is 60 m and its area is 200 sq metres

Question:

The perimeter of a rectangular plot is 60 m and its area is 200 sq metres. Find the dimensions of the plot.

Solution:

Given:
Perimeter of a rectangular plot = 60 m
Area = 200 m2

Let the length of rectangular plot be x m.

Perimeter $=60$

$\Rightarrow 2($ Length $+$ Breadth $)=60$

$\Rightarrow$ Length $+$ Breadth $=30$

$\Rightarrow$ Breadth $=30$ - Length

Then, the breadth is (30 − x) m.

According to the question,

Length $\times$ Breadth $=$ Area

$\Rightarrow x(30-x)=200$

$\Rightarrow 30 x-x^{2}=200$

$\Rightarrow x^{2}-30 x+200=0$

$\Rightarrow x^{2}-10 x-20 x+200=0$

$\Rightarrow x(x-10)-20(x-10)=0$

$\Rightarrow(x-10)(x-20)=0$

$\Rightarrow x=10,20$

For $x=10$

$30-x=20$

For $x=20$

$30-x=10$

Hence, the dimensions of the plot are 10 m and 20 m.