The sides of a triangle are in the ratio 1 2 : 1 3 : 1 4 and its perimeter is 104 cm. The length of the longest side (in cm) is -

Answer: Option C

$$\begin{array}{rl}& \text{Ratio of sides}\\ & =\frac{\text{1}}{\text{2}}:\frac{\text{1}}{\text{3}}:\frac{\text{1}}{\text{4}}\\ & =6:4:3\end{array}$$
Let the sides be 6x, 4x and 3x
Then,
⇒ 6x + 4x + 3x = 104
or 13x = 104
or x = 8
∴ Longest side = 6x = (6 × 8)m = 48m