The altitude of an equilateral triangle with a side length of 4 cm is 2√3 cm.
Here's how to calculate it:
- Understanding Altitude: The altitude of a triangle is a perpendicular line drawn from a vertex to the opposite side. In an equilateral triangle, the altitude bisects the base, creating two 30-60-90 right triangles.
- 30-60-90 Triangle Properties: In a 30-60-90 triangle, the sides are in a specific ratio: 1:√3:2. The hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.
- Calculation:
- The base of each 30-60-90 triangle is half the side length of the equilateral triangle, which is 2 cm.
- The altitude is the longer leg of the 30-60-90 triangle.
- Using the ratio, the altitude is √3 times the shorter leg (2 cm), which is 2√3 cm.
Therefore, the altitude of an equilateral triangle with a side length of 4 cm is 2√3 cm.
