To find the perimeter of an equilateral triangle when the height is given, we can follow a series of steps. Let’s break it down.
1. **Understanding the Relationship Between Height and Side Length**: In an equilateral triangle, the height can be related to the side length using the formula:
Height (h) = (√3 / 2) * Side Length (s)
2. **Substituting the Given Height**: We know that the height of our triangle is 4√3. So we can set up the equation:
4√3 = (√3 / 2) * s
3. **Solving for the Side Length (s)**: To isolate s, we can multiply both sides by 2:
8√3 = √3 * s
4. **Dividing Both Sides by √3**: Now, we can divide both sides by √3 to find s:
s = 8
5. **Calculating the Perimeter**: The perimeter (P) of an equilateral triangle is simply three times the length of one side:
P = 3 * s
Substituting the value of s we found:
P = 3 * 8 = 24
Thus, the perimeter of the equilateral triangle is 24 units.