Question

for each set of three lengths, determine if they can be the side lengths of a triangle.
lengths\tcan be side lengths of a triangle\tcannot be side lengths of a triangle
4, 13, 20\t○\t○
7, 22, 7\t○\t○
7.7, 10.7, 3.9\t○\t○
9, 10, 18\t○\t○

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.

Step 1: Analyze 4, 13, 20

Check the sums:

• \(4 + 13 = 17\), and \(17 < 20\). So, these lengths cannot form a triangle.

Step 2: Analyze 7, 22, 7

Check the sums:

• \(7 + 7 = 14\), and \(14 < 22\). So, these lengths cannot form a triangle.

Step 3: Analyze 7.7, 10.7, 3.9

Check the sums:

• \(7.7 + 3.9 = 11.6\), and \(11.6 > 10.7\)
• \(7.7 + 10.7 = 18.4\), and \(18.4 > 3.9\)
• \(10.7 + 3.9 = 14.6\), and \(14.6 > 7.7\)

So, these lengths can form a triangle.

Step 4: Analyze 9, 10, 18

Check the sums:

• \(9 + 10 = 19\), and \(19 > 18\)
• \(9 + 18 = 27\), and \(27 > 10\)
• \(10 + 18 = 28\), and \(28 > 9\)

So, these lengths can form a triangle.

Answer:

Lengths	Can be side lengths of a triangle	Cannot be side lengths of a triangle
7, 22, 7	○ (No)	○ (Yes)
7.7, 10.7, 3.9	○ (Yes)	○ (No)
9, 10, 18	○ (Yes)	○ (No)

(Note: For each row, mark the appropriate column with a filled circle (e.g., if it can be a triangle, fill the "Can be..." column, else fill the "Cannot be..." column))