Question

press an item in the answer box, and then press on the box in the corresponding category. to remove an item, you can press on the box and the trash can icon to the right of the item you want to remove. side lengths that form a triangle side lengths that do not form a triangle add an answer item! add an answer item! answer bank 6, 2.8, 9 3, 5, 7 4, 4.5, 1 1, 2, 3

Explanation:

To determine which side lengths form a triangle, we use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 1: Analyze \(6, 2.8, 9\)

• \(6 + 2.8 = 8.8\), and \(8.8 < 9\). So, these do not form a triangle.

Step 2: Analyze \(3, 5, 7\)

• \(3 + 5 = 8 > 7\)
• \(3 + 7 = 10 > 5\)
• \(5 + 7 = 12 > 3\). So, these form a triangle.

Step 3: Analyze \(4, 4.5, 1\)

• \(4 + 1 = 5 > 4.5\)
• \(4 + 4.5 = 8.5 > 1\)
• \(1 + 4.5 = 5.5 > 4\). So, these form a triangle.

Step 4: Analyze \(1, 2, 3\)

• \(1 + 2 = 3\), and \(3 = 3\) (not greater). So, these do not form a triangle.

Side lengths that form a triangle:

• \(3, 5, 7\)
• \(4, 4.5, 1\)

Side lengths that do not form a triangle:

• \(6, 2.8, 9\)
• \(1, 2, 3\)

If we were to fill the boxes:

• For "side lengths that form a triangle", add \(3, 5, 7\) and \(4, 4.5, 1\).
• For "side lengths that do not form a triangle", add \(6, 2.8, 9\) and \(1, 2, 3\).

Answer:

To determine which side lengths form a triangle, we use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the remaining side.

Step 1: Analyze \(6, 2.8, 9\)

• \(6 + 2.8 = 8.8\), and \(8.8 < 9\). So, these do not form a triangle.

Step 2: Analyze \(3, 5, 7\)

• \(3 + 5 = 8 > 7\)
• \(3 + 7 = 10 > 5\)
• \(5 + 7 = 12 > 3\). So, these form a triangle.

Step 3: Analyze \(4, 4.5, 1\)

• \(4 + 1 = 5 > 4.5\)
• \(4 + 4.5 = 8.5 > 1\)
• \(1 + 4.5 = 5.5 > 4\). So, these form a triangle.

Step 4: Analyze \(1, 2, 3\)

• \(1 + 2 = 3\), and \(3 = 3\) (not greater). So, these do not form a triangle.

Side lengths that form a triangle:

• \(3, 5, 7\)
• \(4, 4.5, 1\)

Side lengths that do not form a triangle:

• \(6, 2.8, 9\)
• \(1, 2, 3\)

If we were to fill the boxes:

• For "side lengths that form a triangle", add \(3, 5, 7\) and \(4, 4.5, 1\).
• For "side lengths that do not form a triangle", add \(6, 2.8, 9\) and \(1, 2, 3\).