A triangle has integer length sides. If two sides of the triangle are 11 and 19, how many possible lengths are there for the third side?

Guest Nov 21, 2020

#1**+1 **

Using the triangle inequality that says the sum of any two side lengths of a triangle is greater than the remaining side....

1) 11 + 19 .....the missing side must not exceed 29

2 ) 11 + missing side > 19 .....the missing side must be 9 (or greater)

Putting these together, we have that

9 ≤ missing side ≤ 29

Number of possible lengths = 29 - 9 + 1 = 21

CPhill Nov 21, 2020