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?
+128408 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
