Question

Steven is cutting an 11 ft piece of lumber into three pieces to build a triangular garden. Which diagram shows a way in which he can cut the wood to create three pieces that can form a triangle?

A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet.
A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet.
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet.
A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.

Answer 1

Use the triangle inequality: the longest piece must be shorter than the sum of the other two.

Check each:
- 2, 2, 7: 7 ≥ 2+2 (7 ≥ 4) → no
- 1, 4, 6: 6 ≥ 1+4 (6 ≥ 5) → no
- 3, 2, 6: 6 ≥ 3+2 (6 ≥ 5) → no
- 3, 4, 4: 4 < 3+4 (4 < 7) → yes

So the diagram with pieces 3 ft, 4 ft, and 4 ft works.