Question

Lena is building a triangular garden. She has three pieces of fencing: one that is 8 feet long, one that is 6 feet long, and one that is 4 feet long.

Part 1: Use the Triangle Inequality Theorem to check if Lena can create a triangle with these three pieces of fencing.

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.

Will the lengths of fencing that Lena has work to create a triangle?

(3 points)
According to the Triangle Inequality Theorem, will Lena be able to build a triangle using the pieces of fencing she has?

Answer 1

Yes. Check each pair:

- 8 + 6 = 14 > 4
- 8 + 4 = 12 > 6
- 6 + 4 = 10 > 8

All three inequalities hold, so Lena can build a triangle with the pieces.