Question

select the correct answer from each drop - down menu.
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.
amanda should use the three wooden planks of lengths,, and.

Explanation:

Step1: Apply triangle - inequality theorem

The triangle - inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).
Let's check all combinations:

• Combination 1: \(1\), \(3\), \(5\)

\(1+3 = 4<5\), so this combination does not form a triangle.

• Combination 2: \(1\), \(3\), \(6\)

\(1 + 3=4<6\), so this combination does not form a triangle.

• Combination 3: \(1\), \(5\), \(6\)

\(1+5 = 6\), and for a triangle \(a + b>c\) (strict inequality), so this combination does not form a triangle.

• Combination 4: \(3\), \(5\), \(6\)

\(3+5=8>6\), \(3 + 6=9>5\), \(5+6 = 11>3\)

Answer:

\(3\) feet, \(5\) feet, \(6\) feet