If one side of a triangle is of length x and another side is of length x+6,which of the following could not be the lenght of the third side?
a.5
b.7
c.9
d.11
e.13
To determine which of the given lengths could not be the length of the third side of the triangle, we can use the triangle inequality theorem. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let x represent the length of one side of the triangle, and x + 6 represent the length of the other side. The third side could have a length between |x - (x + 6)| and (x + x +6).
So, the range of possible lengths for the third side would be from 6 to 2x + 6.
Now we can check each given length to see if it falls within this range:
a. 5: 5 is less than 6, so it cannot be the length of the third side.
b. 7: 7 is within the range of 6 to 2x + 6, so it could be the length of the third side.
c. 9: 9 is within the range of 6 to 2x + 6, so it could be the length of the third side.
d. 11: 11 is within the range of 6 to 2x + 6, so it could be the length of the third side.
e. 13: 13 is greater than 2x + 6, so it cannot be the length of the third side.
Therefore, the length that could not be the length of the third side is answer choice (e) 13.