Kenneth S. answered • 04/29/16

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Smallest: 5

Largest 17.

How to figure Largest: Suppose that the largest 3rd side lies horizontally & the two other sides, anchored to the endpoints of the largest side, are 7 & 11 in length. Their sum, 18, must exceed the 3rd sides length--otherwise the 7 & 11 lengths cannot meet at a point above the 3rd side (the alligator short leg syndrome).

How to figure Smallest: Begin with an angle whose sides are segments of length 7 & 11. Experiment with small lengths for the other side. If we choose 5, then the two smaller are 7 and 5, and this sum must exceed 11, which it does by the minimum amount, to form a valid triangle. Any lesser choice violates the credo that the two smaller sides must total more than the longest side (triangle inequality property).