Question 756299: The congruent sides of an isosceles triangle have length t. The third side of the isosceles triangle has a length of 19. What is the smallest possible integer value for t?
Answer by algebraic penguin(13)   (Show Source):
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By the triangle inequality, the sum of the lengths of the two sides of a triangle must be more than the length of the third side.
We are trying to minimize t, so it is safe to say that the minimum of t exists when the side with length 19 is the longest side.
We get t+t>19 from the triangle inequality, so 2t>19, so t>9.5,
Since t is an integer, the smallest possible integer value of t is 10.
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