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

A. 26

B. 32

C. 48

D. 52

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & {\text{Ratio of sides}} \cr & = \frac{{\text{1}}}{{\text{2}}}:\frac{{\text{1}}}{{\text{3}}}:\frac{{\text{1}}}{{\text{4}}} \cr & = 6:4:3 \cr} $$
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