SOLUTION: The lengths of two sides of a triangle are 12 miles and 19 miles. Which set of lengths could represent the possible length of the third side, t?

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Question 292549: The lengths of two sides of a triangle are 12 miles and 19 miles. Which set of lengths could represent the possible length of the third side, t?

Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Take two strips of paper.
One 12 units long and one 19 units long.
Connect them together at one point.
Now you can vary the angle of that connection.
The angle can vary from zero to 180 degrees.
At zero, the 12 unit paper lays over the 19 unit paper.
If the angle was just slightly non-zero, the length of the imaginary line connect the 12 and 19 unit pieces would be 7 units long.
Now do the same at 180 degrees.
At slightly less than 180 degrees, the length of the imaginary line would be (12+19=)31 units.
Since in a triangle the angles must sum to 180, the actual angle must be between 0 and 180 degrees.
So then the final length would be between 7 units and 31 units long.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Longest possible length: 12+19=31

Shortest possible length: 19-12=7

Note: A drawing may help to see why these are the possible lengths.