Discover
Can you make a triangle from sticks of 2 cm, 3 cm and 7 cm?
- No
- Yes
Key idea
The triangle inequality.
Three lengths make a triangle only if the two shorter ones add to more than the longest. So a third side lies strictly between the difference and the sum of the other two: .
Worked example
Sides 8 and 5.
Third side
Difference.
Third side
Sum.
From 4 to 12
Whole numbers.
Your turn, guided
Your turn: sides 10 and 4. The largest whole-number third side.
Less than 14.
Practice ★
- Can three sticks of lengths 8, 9 and 18 cm form a triangle?
- No: the two shorter sticks are too short to meet
- Yes: any three lengths make a triangle
- Only as a right triangle
- Can three sticks of lengths 9, 2 and 12 cm form a triangle?
- No: the two shorter sticks are too short to meet
- Yes: any three lengths make a triangle
- Only as a right triangle
- Two sides of a triangle are 15 cm and 3 cm. What is the largest possible whole-number length of the third side?
Watch out!
Practice ★★
- Two sides of a triangle are 14 cm and 4 cm. What is the smallest possible whole-number length of the third side?
- Two sides of a triangle are 6 cm and 4 cm. What is the smallest possible whole-number length of the third side?
Exit ticket
Three questions to check you have got it.
- Two sides of a triangle are 15 cm and 3 cm. What is the largest possible whole-number length of the third side?
- Two sides of a triangle are 6 cm and 3 cm. What is the largest possible whole-number length of the third side?
- Two sides of a triangle are 15 cm and 4 cm. What is the largest possible whole-number length of the third side?
Summary card
Building triangles
Two shorter sides must add to more than the longest.
Watch out: equal is not enough.
End of the lesson
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