To solve this problem, we can use the relationship between the side length $s$ of an equilateral triangle and its altitude $h$.

For an equilateral triangle, the altitude divides the triangle into two 30-60-90 right triangles. In such a triangle:

• The altitude $h$ is related to the side $s$ by the formula: $h = \frac{\sqrt{3}}{2} \times s$ Given that the altitude $h = 14$ cm, we can solve for $s$ (the side of the triangle):

$14 = \frac{\sqrt{3}}{2} \times s$

Now, let's solve for $s$.The side length of the equilateral triangle is approximately $16.17 \, \text{cm}$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the area of an equilateral triangle with the same side length?
2. How do you derive the formula for the altitude of an equilateral triangle?
3. Can you calculate the perimeter of the triangle given the side length?
4. How does the altitude relate to the angles in a 30-60-90 triangle?
5. What is the height of an equilateral triangle with a side length of 10 cm?

Tip: In equilateral triangles, the altitude also bisects the base and the vertex angle, making it a key part of many geometric calculations.