How many isosceles triangles with whole-number length sides have a perimeter of 30 units?
How many isosceles triangles with whole-number length sides have a perimeter of 30 units?
Well, first, for the equal sides to be whole numbers, their total has to be even. That narrows it down.
Let's make a little table.
size of base size of each of the other two sides
2 14 2 + 14 + 14 = 30
4 13 4 + 13 + 13 = 30
6 12
8 11
10 10
12 9
14 8
16 7 This one can't work, nor any subsequent sizes in this progression, because
the sum of any two sides of a triangle has to be larger than the third side.
So it looks like there are seven (7) such isoceles triangles that satisfy the criteria of the problem.
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