Question

how many different triangles can be made have a perimeter of 8 units and all side lengths are inegers

Answer 1

the answer is ..........

triangles with a perimeter of 8 units have side lengths as integers

To Find : How many such triangles possible

Solution:

triangles with a perimeter of 8 units

Possible triplets having sum  8

1 , 1  , 6  

1 ,  2 , 5

1 , 3 , 4

2  , 2 , 4

2 , 3 , 3  

Now in any triangle sum of any two sides is greater than third side

1 + 1 = 2 <  6  hence  1 , 1 , 6 can not be triangle

1 + 2 = 3 < 5  hence  1 , 2 , 5 can not be triangle

1 + 3 = 4  = 4  Hence 1 , 3 , 4 can not be triangle

2 + 2  = 4 = 4 hence 2 , 2 , 4  can not be triangle

2 + 3 = 5 > 3

3 + 3 = 6 > 2

2 , 3 , 3  is the only possible triangle  

only 1 triangle with a perimeter of 8 units have side lengths as integers   .............

hence 2,3,3, is the possible triangle ......

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