Question

Amanda is building a soft triangular kennel for her dog. She has four wooden planks of lengths 1 foot, 3 feet, 5 feet, and 6 feet. Determine which planks Amanda should use to build the triangular-shaped kennel. Enter the lengths from least to greatest.

Answer 1

• 3 feet
• 5 feet
• 6 feet

Explanation:

Given lengths (in feet) of 1, 3, 5, 6, you want to know which three of them will form a triangle.

Triangle inequality

The differences between adjacent lengths are 3-1 = 2, 5-3 = 2, 6-5 = 1. The shortest side must be longer than the difference in lengths between the other two sides. Hence the 1 foot plank cannot be used. (It is not longer than either 1 or 2 feet.)

The remaining three planks satisfy the triangle inequality:

3 + 5 > 6

3 + 6 > 5

5 + 6 > 3

Amanda should use the planks that are 3 feet, 5 feet, and 6 feet long.