The Triangle Inequality theorem states that:
“The sum of the lengths of any two sides of a triangle is greater than the length of the third side.”
Otherwise, a triangle cannot be created.
Below is triangle ABC, with sides AB, BC and AC.
According to triangle inequality theorem,
AB + BC > AC
AC + BC > AB
AC + AB > BC
Example 1:
Could a triangle have sides of lengths 4, 5 and 8?
4 + 5 > 8
5 + 8 > 4
4 + 8 > 5
As all three combinations satisfy the theorem the triangle is possible.
Example 2:
Could a triangle have sides of lengths 2, 5 and 8?
2 + 8 > 5 X
2 + 5 > 8 X
5 + 8 > 2
If any of the combinations does not satisfy the theorem the triangle cannot be created of given lengths.
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