Question

A rectangular field is five times as long as it is wide. If the perimeter of the field is $288\mathrm{yards}$, What are the field's dimensions?

Answer 1

Finding the required dimensions of field:

Given: Perimeter $=288\mathrm{yards}$

Let the width of the field be $\mathrm{w}\mathrm{yards}$

Then according to question, length of the field $=5\mathrm{w}\mathrm{yards}$

Now, perimeter of field $=2\left(5\mathrm{w}+\mathrm{w}\right)$ $[\because$Perimeter of rectangle $=2\left(\mathrm{l}+\mathrm{w}\right),\mathrm{l}$ is the length of the field and $\mathrm{w}$ is the width of the rectangle$]$

$\Rightarrow$ $288=2\left(6\mathrm{w}\right)$

$\Rightarrow$ $288=12\mathrm{w}$

$\Rightarrow$ $24=\mathrm{w}$

So, length of the field $=5\left(24\right)$

$\Rightarrow$ $=120\mathrm{yards}$

Hence, the dimensions of the field are $120\mathrm{yards}\times 24\mathrm{yards}$.