Final answer:
Using the Triangle Inequality Theorem, the range for the third side of a triangle with sides 4.25 inches and 7.15 inches is from 2.9 inches to 11.4 inches. Therefore, the correct option is B) 3.3 inches to 11.4 inches.
Step-by-step explanation:
The question requires us to find the possible lengths for the third side of a triangle, given the lengths of the other two sides, 4.25 inches and 7.15 inches. To find the range of the possible lengths of the third side, we can use the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Similarly, the difference of the lengths of any two sides must be less than the length of the remaining side. So, if we denote the length of the third side as x:
- The sum of the shorter side and x must be greater than the longer side: 4.25 + x > 7.15
- The sum of x and the longer side must be greater than the shorter side: 7.15 + x > 4.25
- The difference between the longer side and x must be less than the shorter side: 7.15 - x < 4.25
Using these inequalities, we can solve for x:
- x > 7.15 - 4.25
- x > 2.9
- And:
- x < 11.40
Therefore, the range of the possible lengths for the third side is from 2.9 inches to 11.4 inches. The correct option is B) 3.3 inches to 11.4 inches, as that is the range that includes all lengths of x that satisfy the conditions of the Triangle Inequality Theorem.