Triangle Side Inequalities
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
1) AB + BC > AC
2) AB + AC > BC
3) AC + BC > AB
Notice in the figure that as vertex C moves closer and closer to side AB, the sum of the lengths of sides AC and CB gets smaller.
Can it ever reach the point where AC+CB=AB? Yes, but then it is no longer a triangle. It would be a straight line!. If AC + CB is not greater than AB, then the sides are not longer enough to make a triangle.
Is a triangle with these three sides possible?
a. 12, 13, 21
b. 7, 8, 15
Solution:
a. 25>21. Yes.
b. 15 = 15. No.
A triangle has two sides of length 4cm and 12 cm. Describe the possible length of the third side, x.
Solution:
There are several possibilities:
But all of them must verify the triangle side inequalities:
x+4>12, then x>8
x+12>4, then x>-8
4+12>x, then 16>x
Consequently 16 > x > 8
