Mathematics
Mathematics
Problem
A student claims, "In every triangle, at least two sides are equal." Give a set of three whole-number side lengths (in centimetres) that form a triangle and explain briefly why your example invalidates the claim.Intuitive explanation
The key insight is that scalene triangles exist—triangles where all three sides have different lengths. To invalidate the claim, you just need to find one counterexample: three whole numbers that satisfy the triangle inequality (the sum of any two sides exceeds the third) but are all distinct. This single example proves the claim false.
Intuitive explanation
The key insight is that scalene triangles exist—triangles where all three sides have different lengths. To invalidate the claim, you just need to find one counterexample: three whole numbers that satisfy the triangle inequality (the sum of any two sides exceeds the third) but are all distinct. This single example proves the claim false.