Question

The length of a rectangular plot is$10\mathrm{m}$ more than its breadth and if the length of its fence is $22\mathrm{m}$ less than $5$ times the breadth, find the dimensions of the rectangular plot.

Answer 1

Find the length and breadth of the rectangular plot.

Step1: Form the equation.

Let the breadth of the rectangular plot be$x$ and the length of the rectangular plot be $x+10$.

The length of its fence is $22\mathrm{m}$ less than $5$ times the breadth$=5x-22$ (given)

$$\begin{gathered} \mathrm{Perimeter}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{plot}=2\left(\mathrm{length}+\mathrm{breadth}\right) \\ 5x-22=2\left[\left(\mathrm{x}+10\right)+\mathrm{x}\right] \end{gathered}$$

Step2: Find the value of$x$

$$\begin{gathered} 5x-22=2\left[\left(x+10\right)+x\right] \\ 5x-22=2\left[2\mathrm{x}+10\right] \\ 5x-22=4x+20 \\ 5x-4x=20+22 \\ \therefore x=42 \end{gathered}$$

$\therefore$The breadth of the rectangular plot is $x=42m$

and the length of the rectangular plot is $x+10=42+10=52m$

$\therefore$The breadth and length of the rectangular plot are $42m$ and $52m$.