SOLUTION: All sides of a triangle are integers. If the length of 2 sides are 7 and 5, what is the largest possible perimeter? I think it is 24, but there is no answer like that in the multi

Question 377826: All sides of a triangle are integers. If the length of 2 sides are 7 and 5, what is the largest possible perimeter?
I think it is 24, but there is no answer like that in the multiple choice. The teacher might have made a mistake(she admitted it herself) but I want to be completely sure that my answer 24 is correct before telling her of her mistake.
Thank you very much.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Imagine this:
If you were to lay the two given sides flat so they form a single contiguous straight line, this line would be 12 (5+7) units long. Now you could not possibly make a triangle by adding a third side of 12 units, it would have to be shorter than 12 in order to make a triangle and, since you are dealing with integral sides, the third side could be no longer than 11 units, making the maximum perimeter 7+5+11 = 23 units.
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