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# Geometry

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How many isosceles triangles with whole-number length sides have a perimeter of 30 units?

Nov 6, 2021

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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.

.

Nov 6, 2021