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How many isosceles triangles with whole-number length sides have a perimeter of 20 units?

 May 26, 2024
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How many isosceles triangles with whole-number length sides have a perimeter of 20 units?   

 

        Start with the shortest possible base, then work upwards.    

 

        Base      Sides   

 

            1          9.5     Won't work.  The problem says whole-number length sides.  

            2           9  

            4           8  

            6           7    

            8           6   

          10           5        Won't work.  Triangle Inequality Theorem, which states that    

                                    the sum of any two sides is greater than the third side.     

 

        Looks like the answer is going to be that there are 4 of them.   

.

 May 26, 2024

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