The centre of gravity of an equilateral triangle with each side a is at a distance of ______ from any of the three sides.
Try it first: pick an option, then read the explanation.
Correct answer: B. a/(2√3)
Asked in SSC JE 03/03/2017 (Morning)
Detailed Explanation
The centroid of any triangle is one-third of the height from each side. For an equilateral triangle every side has the same height.
\[ h = \frac{\sqrt3}{2}a,\qquad \bar y = \frac{h}{3} = \frac{\sqrt3\,a}{6} = \frac{a}{2\sqrt3} \approx 0.289a \]
Why “a/(2√3)” Is Correct
The distance is a/(2√3) — the radius of the inscribed circle.
Why the Other Options Are Wrong
- A. √3a/2: √3a/2 is the full height of the triangle.
- C. 2√3a: 2√3a is larger than the triangle itself.
- D. 3√2a: 3√2a is also larger than the triangle.
Key Point
Equilateral triangle: centroid at h/3 = a/(2√3) from each side (in-radius).
Key Concepts for Students
- Distance from each vertex = 2h/3 = a/√3 (circum-radius).
- Centroid of any triangle = intersection of medians.
- I of an equilateral triangle about a centroidal axis = √3a⁴/96.
Practice more: this is question 49 in Bending and Shear Stress MCQs – Part 4. Try the whole set and check every answer instantly.