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:
Answer & explanation
Correct answer: option 4
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