Mack is drawing a triangle. She wants to use the side lengths of 15 in and 8 in for two of her sides.Which of the lengths below could be the third side of Mack's triangle?3 in6 in4 in9 in

To determine the possible lengths of the third side of a triangle, we can use the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

Given that Mack's triangle has sides of 15 in and 8 in, the possible lengths of the third side (let's call it x) must satisfy these two conditions:

1. x < 15 in + 8 in
2. x > 15 in - 8 in

Solving these inequalities gives:

1. x < 23 in
2. x > 7 in

So, the third side of Mack's triangle must be greater than 7 inches and less than 23 inches.

Looking at the options provided:

3 in - This is less than 7 in, so it cannot be the third side. 6 in - This is also less than 7 in, so it cannot be the third side. 4 in - This is less than 7 in, so it cannot be the third side. 9 in - This is greater than 7 in and less than 23 in, so it could be the third side.

Therefore, the only possible length for the third side of Mack's triangle from the options provided is 9 inches.