2019 · Q42
If l is the length of the median of an equilateral triangle, then what is its area?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A√3l²/3
- B√3l²/2
- C√3l²
- D2l²
Explanation
In an equilateral triangle the median is also the altitude: l = (√3/2)a, so the side is a = 2l/√3. The area is (√3/4)a² = (√3/4)(4l²/3) = √3·l²/3. The answer is (A).