Question 514197: A triangle has a base length of 13 and its two ther sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?
Found 2 solutions by xdragonfight, MathTherapy:
Answer by xdragonfight(116)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
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A triangle has a base length of 13 and its two ther sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side?
Based on the triangular inequality theorem, a side of a triangle ranges from a value that is more than the difference of the other two sides but less than their sum.
Let one of the equal sides be S
Then the other = S
In this case, since the unequal base side = 13, then one of the equal sides, or S > 13 - S
We have: S + S > 13
2S > 13 ------ S > 13/2, or 6.5
Now, since we’re looking for the SMALLEST possible integer, then one of the equal sides will have a value of  (smallest integer > 6.5) units.
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