Study guides › Level 7 · Geometry

Can these sides make a triangle

Level 7 · Geometry · for questions like “Two sides of a triangle are 5 and 9. Which could be the third side?”

💡 The idea

Any two sides together must be longer than the third. So the third side must be:

more than the difference, and less than the sum.

✏️ Worked examples

1. Sides 5 and 9: the third side must be more than 4 and less than 14. So 7 works, but 14 and 4 don't (the triangle would lie flat).

2. Sides 6 and 10, whole numbers only: the longest the third side can be is 15.

⚠️ Watch out

• Equal to the sum doesn't count: the triangle would be squashed flat.

🎯 Try these

1. Sides 3 and 8: could the third side be 5?
2. Sides 7 and 7: the longest whole-number third side?
3. Sides 4 and 11: the shortest whole-number third side?

Answers: 1) No (3 + 5 = 8, flat) 2) 13 3) 8

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.