One side of an equilateral triangle is 24 cm. The midpoints of its sides are joined to form another triangle whose midpoints are in turn joined to form still another triangle this process continues indefinitely. The sum of the perimeters of all the triangles is

Explanation

To solve the problem, we need to find the sum of the perimeters of all the triangles formed by joining the midpoints of the sides of an equilateral triangle with a side length of 24 cm.

### Step-by-Step Solution:

1. **Identify the Side Length of the Original Triangle:**
The side length of the original equilateral triangle \( ABC \) is given as 24 cm.

2. **Calculate the Perimeter of the Original Triangle:**
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