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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?

 Nov 21, 2020
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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

 

cool cool cool

 Nov 21, 2020

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