Centre of gravity of a right-angled triangle A statement claims: “The centre of gravity (centroid) of a right-angled triangle lies at its geometrical centre.” Determine whether this statement is correct or incorrect.

Introduction / Context:In statics and engineering mechanics, the centroid (centre of gravity in a uniform field) of standard plane figures is a frequently used result. Right-angled triangles are common in structural and area-moment problems.

Given Data / Assumptions:

• Uniform thickness and density so CG coincides with geometric centroid.
• Right triangle with legs of lengths b and h meeting at the right angle.

Concept / Approach:The centroid of a triangle lies at the intersection of its medians. For a right-angled triangle, measured from the right-angled vertex along the legs, the centroid coordinates are x̄ = b/3 and ȳ = h/3. This is not the “geometrical centre” in the sense of the midpoint of a bounding rectangle or the triangle’s circumcenter.

Step-by-Step Solution:

Verification / Alternative check:Using area-integration: x̄ = (1/A)∫x dA over the triangular region yields x̄ = b/3 and similarly ȳ = h/3, confirming the standard centroid location.

Why Other Options Are Wrong:

• “Correct” would imply a symmetric centre; a right triangle lacks central symmetry.

Common Pitfalls:Confusing centroid with circumcenter or incenter; these are distinct triangle centres and lie at different locations.

Final Answer:Incorrect