2024 · Q65
Consider the following for the next ten (10) items that follow: Each item contains a Question followed by two Statements. Answer each item using the following instructions: Let a, b and c be the sides of a triangle ABC. Question : Is the triangle equilateral?
Statement Ia² + b² + c² = (ab + bc + ca)
Statement II3a² + 3b² + 4c² = 2ab + 4bc + 4ca
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AIf the Question can be answered by one of the Statements alone, but not by the other.
- BIf the Question can be answered by either Statement alone.
- CIf the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DIf the Question cannot be answered even by using both Statements together.
Explanation
Statement I rearranges to ½[(a−b)² + (b−c)² + (c−a)²] = 0, forcing a = b = c (equilateral). Statement II rearranges to (a−b)² + 2(b−c)² + 2(c−a)² = 0, also forcing a = b = c. Either statement alone answers yes: option (b).