Question

Use the Triangle Inequality Theorem to determine which three side lengths form a triangle. %0D%0A*%0D%0A1 point%0D%0A2, 7, 9%0D%0A7, 8, 9%0D%0A7, 5, 13%0D%0A4, 15, 20

Answer 1

To determine which three side lengths form a triangle, we need to compare each side length to the sum of the other two side lengths.

1. For the first set of side lengths (2, 7, 9):
- 2 + 7 = 9, so the sum of the two smaller sides is equal to the largest side.
- 7 + 9 = 16 and 2 + 9 = 11, so the sum of the two larger sides is greater than the smallest side.
- 2 + 9 = 11 and 2 + 7 = 9, so the sum of the smallest side and one other side is less than the remaining side.

Since all three conditions are met, the side lengths 2, 7, 9 can form a triangle.

2. For the second set of side lengths (7, 8, 9):
- 7 + 8 = 15, which is less than 9, so the sum of the two smaller sides is not greater than the largest side.

Since the first condition is not met, the side lengths 7, 8, 9 cannot form a triangle.

3. For the third set of side lengths (7, 5, 13):
- 5 + 7 = 12 and 5 + 13 = 18, so the sum of the two smaller sides is less than the largest side.

Since the first condition is not met, the side lengths 7, 5, 13 cannot form a triangle.

4. For the fourth set of side lengths (4, 15, 20):
- 4 + 15 = 19, which is less than 20, so the sum of the two smaller sides is not greater than the largest side.

Since the first condition is not met, the side lengths 4, 15, 20 cannot form a triangle.

Therefore, the side lengths that form a triangle are 2, 7, 9.