Final answer:
The range of possible lengths for the third side of the triangle is 1 ft to 25 ft.
Step-by-step explanation:
To find the range of possible lengths for the third side of a triangle when the lengths of two sides are given, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, in this case, we have two sides with lengths 12 ft and 13 ft. To find the range of possible lengths for the third side, we need to find the minimum and maximum values.
To find the minimum value, we subtract the length of the given side with the greatest length from the length of the given side with the smallest length. So, the minimum possible length for the third side is 13 - 12 = 1 ft.
To find the maximum value, we add the lengths of the two given sides. So, the maximum possible length for the third side is 12 + 13 = 25 ft. Therefore, the range of possible lengths for the third side is 1 ft to 25 ft.