Triangle Inequality Theorem – Example

# Triangle Inequality Theorem – Example

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• Example 1
• Example 2
• Summary
• What’s Next?

In the previous segment, we had a look at Triangle Inequality Theorem. In this segment, we will see the examples of the Triangle Inequality Theorem.

## Example 1

Q. Can we form a triangle with lengths 2 cm, 3 cm, and 5 cm?

Solution:

According to the triangle inequality theorem, the sum of any two sides in a triangle will always be greater than the third side of that triangle.

But here 2 + 3 = 5.

Hence, the triangle with these lengths cannot be constructed.

## Example 2

Q. Can we form a triangle with lengths 3 cm, 4 cm, and 5 cm?

Solution:

According to the triangle inequality theorem, the sum of any two sides in a triangle will always be greater than the third side of that triangle.

Here,

3 + 4 > 5

4 + 5 > 3

5 + 3 > 4

Hence, the triangle with these lengths can be constructed.

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