Question : The sides of a triangle are in the ratio $\frac{1}{3}: \frac{1}{5}: \frac{1}{6}$. If the perimeter is 147 cm, then the length of the smallest side is_____.
Option 1: 12 cm
Option 2: 25 cm
Option 3: 30 cm
Option 4: 35 cm
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Correct Answer: 35 cm
Solution : Given that the sides of a triangle are in the ratio $\frac{1}{3}: \frac{1}{5}: \frac{1}{6}$ And Perimeter = 147 cm Let the sides be $\frac{x}{3},$ $\frac{x}{5},$ and $\frac{x}{6}$ According to the question, $\frac{x}{3}+\frac{x}{5}+\frac{x}{6}=147$ ⇒ $\frac{10x+6x+5x}{30}=147$ ⇒ $21x=147\times 30$ ⇒ $x=7\times 30 $ ⇒ $x=210$ cm ⇒ Smallest side = $\frac{x}{6}=\frac{210}{6}=35$ cm Hence, the correct answer is 35 cm.
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