Geometry

 

All the sides of a triangle have integer length.  One of the sides has length $28$.  What is the smallest possible perimeter of the triangle?     

 

By the Triangle Inequality Theorem,     

the smallest sum of the other two sides has to be more than 28.  But the sum cannot be 29     

because then they wouldn't be integers.  So the smallest sum of the other sides must be 30.     

So that makes 28 + 30 = 58 the smallest possible perimeter of the triangle.     

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