Question

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

Answer 1

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

Let the length of rectangular plot be x m.
$$\begin{gathered} \mathrm{Perimeter}=60 \\ \Rightarrow 2\left(\mathrm{Length}+\mathrm{Breadth}\right)=60 \\ \Rightarrow \mathrm{Length}+\mathrm{Breadth}=30 \\ \Rightarrow \mathrm{Breadth}=30-\mathrm{Length} \end{gathered}$$

Then, the breadth is (30 − x) m.

According to the question,

$$\begin{gathered} \mathrm{Length}\times \mathrm{Breadth}=\mathrm{Area} \\ \Rightarrow x\left(30-x\right)=200 \\ \Rightarrow 30x-x^2=200 \\ \Rightarrow x^2-30x+200=0 \\ \Rightarrow x^2-10x-20x+200=0 \\ \Rightarrow x\left(x-10\right)-20\left(x-10\right)=0 \\ \Rightarrow \left(x-10\right)\left(x-20\right)=0 \\ \Rightarrow x=10,20 \\ \mathrm{For}x=10, \\ 30-x=20 \\ \mathrm{For}x=20, \\ 30-x=10 \end{gathered}$$

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