# A triangle has side lengths of 11 cm and 9 cm. Which could be the value of the third side, 20 cm or 15 cm?

Mar 11, 2016

The third side measures 15 cm.

#### Explanation:

By the triangle side length theorem, the sum of the two shorter sides has to be equal to or larger than the third side. Thus, we can write the following inequation.

$a + b \ge c$, where a and b are the shorter sides and c the longest.

11, 9 and 15 satisfies this inequality while 11, 9 and 20 doesn't.

Justification:

The reason for this rule is simple; it's because if the longest side is longer than the sum of the two shorter sides, this means that the shorter sides aren't long enough to connect with the longest side, thus rendering the shape a collection of lines and disqualifying the possibility of having a triangle, which was our objective.

Practice exercises:

1. Which of the following triangles is possible?

a) 4,6 and 14

b) 5,11 and 16

c) 1,3,6

D). 12,19 and 26

1. Find the smallest possible value of a to make the following an actual triangle : $a , 14 , 25$

Hopefully this helps: