The sides of a triangle are in the ratio of $$\frac{2}{5}:\frac{1}{3}:\frac{3}{5}$$​ and its perimeter is 110 cm. The length of the shortest side is:

Correct option is A

Given:

The sides of a triangle are in the ratio $$\frac{2}{5} : \frac{1}{3} : \frac{3}{5}.$$​​

The perimeter of the triangle is 110 cm.

We need to find the length of the shortest side.

Solution:

The given ratio is $$\frac{2}{5} : \frac{1}{3} : \frac{3}{5}.$$​​

​$$\frac{2}{5} = \frac{6}{15}$$​​

​$$\frac{1}{3} = \frac{5}{15}$$​​

​$$\frac{3}{5} = \frac{9}{15}$$​​

So, the ratio of the sides is:

= 6 : 5 : 9

Let the sides of the triangle be 6x, 5x, and 9x.

The perimeter is the sum of the sides:

6x + 5x + 9x = 110

20x = 110

x = $$\frac{110}{20} = 5.5$$​

The shortest side is 5x. Now substitute the value of x:

Shortest side = $$5 \times 5.5 = 27.5 \, \text{cm}$$​
The length of the shortest side is 27.5 cm.