5
lesson pretestMultiple Choice

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Question 5 • 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 line segment is divided by two dashed cut marks into three pieces labeled 1 foot, 4 feet, and 6 feet.
B
Image with description A line segment is divided by two dashed cut marks into three pieces labeled 3 feet, 4 feet, and 4 feet.
C
Image with description A line segment is divided by two dashed cut marks into three pieces labeled 2 feet, 2 feet, and 7 feet.
D
Image with description A line segment is divided by two dashed cut marks into three pieces labeled 3 feet, 2 feet, and 6 feet.

Explanation

For three lengths to form a triangle, the sum of the two shorter sides must be greater than the longest side. In choice B, the two shorter pieces are 3 feet and 4 feet, and 3 + 4 = 7, which is greater than 4 feet. Therefore, the 3-foot, 4-foot, and 4-foot pieces can form a triangle.

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