9
QuizMultiple Choice

Triangles and Their Side Lengths — Quiz

Question 9 • Mathematics II

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?

Answer
A
Image with description A piece of wood is cut into 3 pieces. The pieces are: 2 feet, 2 feet, and 7 feet.
B
Image with description A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 4 feet, 4 feet.
C
Image with description A piece of wood is cut into 3 pieces. The pieces are: 3 feet, 2 feet, and 6 feet.
D
Image with description A piece of wood is cut into 3 pieces. The pieces are: 1 foot, 4 feet, 6 feet.

Explanation

For three lengths to form a triangle, the sum of the two shorter sides must be greater than the longest side. With 3 ft, 4 ft, and 4 ft, the two shorter sides total 7 ft, which is greater than 4 ft, so these pieces can form a triangle. The other choices have two shorter pieces whose sum is not greater than the longest piece.

AI-written and checked against the verified answer.

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