Question 379050: an isosceles triangle has a perimeter of 64.How many different triangles can this be?Give the Dimensions of each.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! I hope you assume the side lengths are integers, otherwise there would be infinitely many triangles.
If the side lengths are integers, the smallest such "base" is 2, resulting in the other sides being 31 and 31. The base must be even, as the other two lengths are equal and are integers. Thus, we have the following sets as side lengths:
(2, 31, 31)
(4, 30, 30)
(6, 29, 29)
.
.
.
(30, 17, 17)
If the base were any larger (e.g. 32, 16, 16) the triangle would either be degenerate or non-existent. This gives us 15 different triangles.
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