The sides of a triangle are in the ratio 12 : 14 : 25 and its perimeter is 25.5 cm.

(c) 12.5 cm

Let the sides of the triangle be 12x cm, 14x cm and 25x cm.
Thus, we have:

Perimeter $=12 x+14 x+25 x$

$\Rightarrow 25.5=51 x$

$\Rightarrow x=\frac{25.5}{51}=0.5$

$\therefore$ Greatest side of the triangle $=25 x=25 \times 0.5=12.5 \mathrm{~cm}$