Question

Triangular inequality theorem practice 7th grade

Answer 1

1. Find the range of possible values for the length of the third side of a triangle when the other two sides have lengths of 5 and 10.

Using the triangular inequality theorem, the third side must satisfy the following inequalities:
- 5 + 10 > third side
- 5 + third side > 10
- 10 + third side > 5

Solving these inequalities:
- 15 > third side
- third side > 5
- 10 > third side

Therefore, the range of possible values for the length of the third side is 5 < third side < 10.

2. Determine if it is possible to form a triangle with sides of lengths 3, 4, and 9.

Using the triangular inequality theorem:
- 3 + 4 > 9 (7 > 9, not satisfied)
- 3 + 9 > 4 (12 > 4, satisfied)
- 4 + 9 > 3 (13 > 3, satisfied)

Since one of the inequalities is not satisfied, it is not possible to form a triangle with sides of lengths 3, 4, and 9.