In the triangle \(ABC\), given:
- The perimeter \(P = 108\) cm
- Side \(AB = 35\) cm
- Side \(CA = 32\) cm
To find the length of side \(BC\), we can use the formula for the perimeter of a triangle:
\[ P = AB + BC + CA \]
Substituting the known values into the formula:
\[ 108 = 35 + BC + 32 \]
Now, combine the known side lengths:
\[ 108 = 67 + BC \]
Next, isolate \(BC\) by subtracting 67 from both sides:
\[ 108 - 67 = BC \]
\[ BC = 41 \text{ cm} \]
Therefore, the length of side \(BC\) is \(41\) cm.