The number of possible triangles with integral sides whose two sides are 5cm, 7cm are   
 

In triangle difference of any two sides must be less than third side 
$\therefore 7-5=2<\mathrm{x}\text{ (where' }\mathrm{x}\text{ ' is the third side) }$
And sum of two sides should be greater than third side (x)
$\begin{array}{l}\therefore 7+5>\mathrm{x}\\ 12>\mathrm{x}\\ \Rightarrow \mathrm{x}<12,\text{ and }\mathrm{x}>2\end{array}$
And given ‘x’ is integer between ‘2’ and ‘12’
$\therefore \left\{3,4,5,6,7,8,9,10,11\right\}$ are the possible values of ‘x’  
Number of triangles are = 9