Answer: Given the lengths of two sides of a triangle, 9 feet, and 16 feet, we can use the triangle inequality theorem to determine the possible lengths of the third side.
The triangle inequality 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. Therefore, if we have the lengths of two sides of a triangle, we can use the following inequality to find the possible lengths of the third side:
a + b > c
Where a and b are the lengths of two known sides of the triangle, and c is the length of the third side.
For the given triangle, with side lengths 9 feet and 16 feet, we can use the inequality to find the possible lengths of the third side:
9 feet + 16 feet > c
25 feet > c
This means that the possible lengths of the third side of the triangle must be less than 25 feet. In other words, any length less than 25 feet would be a valid length for the third side of the triangle.
It is also worth noting that the sides of a triangle can't be negative, so c must be greater than 0 as well.
Step-by-step explanation:
