Centre of gravity (centroid) of an equilateral triangle: distance from any side An equilateral triangular lamina has side length a. Choose the correct perpendicular distance of the centroid from any of its sides.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
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A(√3 a)/6
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B(√3 a)/2
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Ca/(2√3)
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D(√3 a)/3
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Ea/6
Answer
Correct Answer: (√3 a)/6
Explanation
Given data
- Equilateral triangle, side a.
Concept/Approach
- Height h of an equilateral triangle is h = (√3/2)·a.
- The centroid divides the height in the ratio 2:1 from vertex to base, so its distance from a side (the base) equals h/3.
Step-by-step calculationDistance from any side = h/3 = [(√3/2)·a]/3 = (√3 a)/6.
Common pitfalls
- Confusing centroid with incenter or circumcenter distances; only the centroid gives h/3 from each side.
Final Answer(√3 a)/6