Let a = 10 cm, b = 3 cm and c = 6 cm. Which of the following is true?

Concept

Three positive lengths can form a non-degenerate triangle only when the sum of every pair is greater than the third length. It is enough to compare the two smaller lengths with the largest; if their sum is not greater, no triangle can be formed.

Application

1. Order the lengths: 3 cm, 6 cm, 10 cm.

2. Add the two smaller lengths: 3 + 6 = 9 cm.

3. Compare this sum with the largest length: 9 cm < 10 cm, so the strict triangle inequality is not satisfied.

4. Therefore, these lengths do not form a triangle and hence cannot form a right-angled or an isosceles triangle.

Cross-check and contrast

• The basic triangle condition must hold before any special triangle classification can apply.

• A right-angled triangle and an isosceles triangle are both triangles, so each is ruled out when the basic condition fails.

• The claim that more than one listed classification applies is also ruled out.

Result

The true choice is “None of the above.”