The length and breadth of a rectangular field are in the ratio $5:4$. If its perimeter is $108m$, find the dimensions of the field.

Let, the constant term of the ratio be $x$,

Length of the rectangular field $=5x$

The breadth of the rectangular field $=4x$

The perimeter of the rectangular field $=108m$

$2$$($length $+$ breadth$)$ $=108m$

$2(5x+4x)$ $=108m$

$2\times 9x$ $=108m$

$18x$ $=108m$

$x$ $=\frac{108}{18}$

$x$ = $=6$

Length of the rectangular field $=5x$

$=5\times 6m$

$=30m$

Breadth of the rectangular field $=4x$

$=4\times 6m$

$=24m$