apply the triangle inequality theorem to determine the possible whole number measures of the third side
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let the lengths of the two given sides be a and b, and the length of the third side be c.
According to the Triangle Inequality Theorem, we have the following inequality:
a + b > c
Now we can determine the possible whole number measures of the third side by testing different values of c.
For example, if the two given sides are 2 and 3:
2 + 3 > c
5 > c
Therefore, the possible whole number measures of the third side would be any integer greater than 5.
Similarly, for the given sides 4 and 7:
4 + 7 > c
11 > c
Therefore, the possible whole number measures of the third side would be any integer greater than 11.
By applying the Triangle Inequality Theorem in this way, we can determine the possible whole number measures of the third side for any given triangle.