Two sides of a (non-degenerate) triangle are 21 and 27. How many possible lengths are there for the third side, if it is a positive integer?
This has to satisfy the triangle inequality that says that the sum of any two side lengths of a triangle are greater than the remaining side
So...let x be the possible unlnown side lengths.....and we have that
21 + 27 > x and 21 + x > 27
48 > x x > 6
So....the possible side lengths are [ 7 , 47 ]
The number of positive integers = 47 - 7 + 1 = 41