The sum of the lengths of any two sides of a triangle is … the length of the third side.
greater than
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This is known as the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Mathematically, it can be represented as:
a + b > c
b + c > a
a + c > b
where a, b, and c are the lengths of the sides of the triangle. This theorem is essential in geometry and is used to determine whether a given set of side lengths can form a triangle or not.
For example, if we have side lengths of 5, 8, and 15, we can use the triangle inequality theorem to determine whether they can form a triangle or not.
5 + 8 > 15 (true)
8 + 15 > 5 (true)
5 + 15 > 8 (true)
As all three inequalities are true, we can conclude that these side lengths can form a triangle.
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