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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

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