Final answer:
The range of possible whole number measures for the base of an isosceles triangle with leg lengths of 5 feet is between 1 foot and 9 feet inclusive, following the triangular inequality theorem.
Step-by-step explanation:
To determine the range of possible whole number measures for the base of an isosceles triangle with leg lengths of 5 feet, we must consider the properties of triangles. In an isosceles triangle, the two legs are equal in length. The base can be any length that allows for the formation of a triangle, adhering to the triangular inequality theorem which states that the sum of the lengths of any two sides must be greater than the length of the remaining side.
Given that the legs are each 5 feet long, the base must be less than 10 feet because 5 + 5 is greater than any base less than 10. However, the base must also be longer than 0 feet, because any positive number plus 5 is always going to be greater than 5. Therefore, the range of whole number lengths for the base is from 1 to 9 feet inclusive.