Question

Do these sides make a triangle ?

Yes or no

1) 7cm , 11cm , 14cm

2) 10cm , 8cm , 2cm

Answer 1

1. yes
2. no

Explanation:

For three side lengths to form a triangle, the sum of the shorter two must exceed the longest.

__

1)

7 + 11 = 18 > 14 . . . . Will make a triangle.

__

2)

2 + 8 = 10 . . . not greater than 10. Will not make a triangle.

__

This is a direct consequence of the triangle inequality, which requires for sides a, b, c that ...

a +b > c and b +c > a and c +a > b

_____

Additional comment

There is a version of the triangle inequality that uses the ≥ comparison, rather than >. If that is the version of the inequality you are using, then both these sets of lengths will form a triangle. The second "triangle" will look like a line segment and have zero area.