Prove congruence and use it to prove a further result

The two triangular garden sections are compared using the following described data

\(\triangle EGH\) and \(\triangle FHG\)

The measurements use m

The segments EG and FH meet transversal GH

They are not stated to be parallel

The two unshared vertices lie on opposite sides of the shared segment

The data give \(EG = FH = 9\,\mathrm{m}\)

The data give \(EH = FG = 15\,\mathrm{m}\)

Side \(GH\) is shared and has length \(12\,\mathrm{m}\)