The sides of a triangle are in the ratio $\frac{1}{3} : \frac{1}{5} : \frac{1}{4}$ and its perimeter is 141 cm. The difference between the greatest side and the smallest side is:

24 cm

We have,

The ratio of sides of a triangle = \(\frac{1}{3}\) : \(\frac{1}{5}\) : \(\frac{1}{4}\)

Perimeter = 141 cm

According to the question

= \(\frac{a}{3}\) + \(\frac{a}{5}\) + \(\frac{a}{4}\)= 141

= (20a + 12a + 15a)× \(\frac{1}{60}\) = 141

= 47a × \(\frac{1}{60}\) = 141

= 47a = (141 × 60)

= 47a = 8460

= a = 180

Now, The greatest side = \(\frac{a}{3}\) = \(\frac{180}{3}\) = 60 cm

The smallest side = \(\frac{a}{5}\) = \(\frac{180}{5}\) = 36 cm

The difference between greatest side and smallest side = (60 – 36) = 24 cm