Practice Triangle Inequality in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

Try to build a triangle with two short sticks and one very long one—you can't. The two short sticks can't reach across to close the shape. It's like trying to take a shortcut: the direct path (one side) is always shorter than going around (the other two sides combined).

Example 1

easy
Can sides of length 4, 7, and 10 form a triangle? Check all three triangle inequality conditions.

Example 2

medium
Two sides of a triangle have lengths 8 and 13. Find the range of possible lengths for the third side.

Example 3

easy
Which of these sets of side lengths cannot form a triangle? (a) 3, 4, 5. (b) 1, 2, 3. (c) 5, 8, 12.

Example 4

hard
In \triangle ABC, AB = 6 and BC = 10. The perimeter is 24. Is this a valid triangle? Find AC and verify.
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