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? 2 ft 2 ft 7 ft; 1 ft 4 ft 6 ft; 3 ft 2 ft 6 ft; 3 ft 4 ft 4 ft

Explanation:

To determine if three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the remaining side. We check each option:

Step 1: Check the first option (2 ft, 2 ft, 7 ft)

• \(2 + 2 = 4\), and \(4 < 7\). This does not satisfy the triangle inequality theorem.

Step 2: Check the second option (1 ft, 4 ft, 6 ft)

• \(1 + 4 = 5\), and \(5 < 6\). This does not satisfy the triangle inequality theorem.

Step 3: Check the third option (3 ft, 2 ft, 6 ft)

• \(3 + 2 = 5\), and \(5 < 6\). This does not satisfy the triangle inequality theorem.

Step 4: Check the fourth option (3 ft, 4 ft, 4 ft)

• \(3 + 4 = 7\), and \(7 > 4\)
• \(3 + 4 = 7\), and \(7 > 4\)
• \(4 + 4 = 8\), and \(8 > 3\)

All three conditions of the triangle inequality theorem are satisfied.

Answer:

The diagram with lengths 3 ft, 4 ft, and 4 ft (the fourth option) shows a way to cut the wood to form a triangle.