The sides of a triangle are consecutive integers. The perimeter of the triangle is 120 cm. Find the length of the greatest side :

Answer: Option C

Let the sides of the triangles be x cm, (x + 1) cm and (x + 2) cm respectively.
Then,
$$\begin{array}{rl}& x+\left(x+1\right)+\left(x+2\right)=120\\ & \Rightarrow 3x+3=120\\ & \Rightarrow 3x=117\\ & \Rightarrow x=39\end{array}$$
∴ Length of greatest side :
= (39 + 2) cm
= 41 cm