Question

If the ratio between the length and perimeter of a rectangular plot is 1 : 3, then the ratio between the length and breadth of the plot is
(a) 1 : 2
(b) 2 : 1
(c) 3 : 2
(d) 2 : 3

Answer 1

(b) 2 : 1
Let the breadth of the plot be b cm.

Let the length of the plot be x cm.
Perimeter of the plot = 3x cm

Perimeter of the plot =2(Length + Breadth)= 2(x + b) cm
$$\begin{gathered} \Rightarrow 2(x+b)=3x \\ 2x+2b=3x \\ \Rightarrow 2b=3x-2x \\ \Rightarrow 2b=x \\ \Rightarrow b=\frac{x}{2} \\ \therefore \mathrm{Ratio}o\mathrm{f}\mathrm{the}\mathrm{length}\mathrm{and}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{plot}=\frac{\mathrm{x}}{\left({\displaystyle \frac{\mathrm{x}}{2}}\right)}=\frac{\mathrm{x}}{\mathrm{x}}\times 2=\frac{2}{1} \\ \therefore \mathrm{Ratio}\mathrm{of}\mathrm{the}\mathrm{length}\mathrm{and}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{plot}=2:1 \end{gathered}$$