Question

Difference of two sides of a triangle is always _______ than the third side.

• A. Greater
• B. Lesser
• C. Equal
• D. Not sure

Answer 1

The correct option is B Lesser

Difference of two sides of a triangle is always lesser than the third side.
Proof:
Start with the Triangle Inequality Theorem which is, the sum of any two sides of a triangle must be greater than the third. Stated algebraically:
Let A, B and C be the sides of the triangle.
A < B + C
B < A + C
C < A + B

1. Subtract B from both sides, then A - B < C
2. Subtract C from both sides, then B - C < A
3. Subtract A from both sides, then C - A < B