Triangle Inequality Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyCan sides of length 4, 7, and 10 form a triangle? Check all three triangle inequality conditions.
Solution
- 1 Step 1: The Triangle Inequality Theorem states that the sum of any two sides must be greater than the third side. Check all three combinations.
- 2 Step 2: ✓
- 3 Step 3: ✓
- 4 Step 4: ✓ All three conditions are satisfied.
Answer
Yes, sides 4, 7, and 10 can form a triangle.
The Triangle Inequality requires all three pairwise sums to exceed the remaining side. In practice, only the sum of the two shortest sides needs to exceed the longest side — if that holds, the other two conditions are automatically satisfied. Here, is the critical check.
About Triangle Inequality
The sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.
Learn more about Triangle Inequality →More Triangle Inequality Examples
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 easyWhich of these sets of side lengths cannot form a triangle? (a) 3, 4, 5. (b) 1, 2, 3. (c) 5, 8, 12.
Example 4 hardIn [formula], [formula] and [formula]. The perimeter is 24. Is this a valid triangle? Find [formula]