Hi

if an isosceles triangle has a perimeter of 24 units, 

what is a possible set of lengths of all three sides: 10, 10 , 4 

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
 Let's determine first what the largest possible measure each of 

the two congruent legs can have:



The smallest the base can be is 1, so the two congruent legs

would have length  or maximum  each if the length an integer



Now we will determine what the smallest possible measure each of 

the two congruent legs can have:



If the two legs are "" units each and the base is , then by the

triangle inequality:



(1)               

 

and since the perimeter , 



               



(2)                 



Substitute the  for  in equation (1)



                   



                   



                   



                    



                    



Therefore the smallest "" can be is  to : ,,,, and .



and, since , "" can range from   to : "" can be ,,,, and .



So there are  5 possible triangles.  Here they all are:



                  

1. sides , , 

2. sides , ,

3. sides , , 

4. sides , , 

5. sides , , 

 

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