What is the length of the altitude of an equilateral triangle having 144 cm as its side ?

Answer

To find the length of the altitude of an equilateral triangle with a side length of 144 cm, we can follow these steps:

### Step 1: Understand the properties of an equilateral triangle
An equilateral triangle has all three sides equal and all three angles equal to 60 degrees. The altitude (height) of the triangle divides it into two 30-60-90 right triangles.

### Step 2: Use the formula for the altitude of an equilateral triangle
The formula for the altitude (h) of an equilateral triangle with side length (a) is given by:
\[ h = \frac{\sqrt{3}}{2} \times a \]

### Step 3: Substitute the value of the side length into the formula
Given that the side length \( a = 144 \) cm, we can substitute this value into the formula:
\[ h = \frac{\sqrt{3}}{2} \times 144 \]

### Step 4: Calculate the altitude
Now, we can calculate the altitude:
\[ h = \frac{\sqrt{3}}{2} \times 144 \]
\[ h = 72\sqrt{3} \]

### Step 5: Approximate the value of \( \sqrt{3} \)
Using the approximate value of \( \sqrt{3} \approx 1.732 \):
\[ h \approx 72 \times 1.732 \]
\[ h \approx 124.97 \text{ cm} \]

### Step 6: Final answer
Thus, the length of the altitude of the equilateral triangle is approximately:
\[ h \approx 125 \text{ cm} \]