Question

For each of the following, determine whether or not it is possible to draw a triangle with sides of the given measure. Write 'Yes' or 'No' and verify with an inequality.

1. 1 cm, 2 cm, and 3 cm (No, because 1 + 2 < 3)
2. 11 ft, 12 ft, and 17 ft (Yes, because 11 + 12 > 17)
3. 2.5 m, 6 m, and 6.5 m (Yes, because 2.5 + 6 > 6.5)
4. 9 yd, 40 yd, and 41 yd (Yes, because 9 + 40 > 41)
5. 16 m, 12 m, and 17 m (Yes, because 16 + 12 > 17)
6. 4.7 cm, 9 cm, and 4.1 cm (No, because 4.7 + 4.1 < 9)
7. 2.2 ft, 12 ft, and 14.3 ft (Yes, because 2.2 + 12 > 14.3)
8. 20 yd, 48 yd, and 52 yd (Yes, because 20 + 48 > 52)
9. 14 in., 15 in., and 30 in. (No, because 14 + 15 < 30)
10. 2.3 m, 12 m, and 12.2 m (No, because 2.3 + 12 < 12.2)
11. 215 cm, 204 cm, and 7 cm (No, because 215 + 204 < 7)
12. 100 in., 100 in., and 5 in. (No, because 100 + 100 < 5)
13. 3 cm, 4 cm, and 7 cm (No, because 3 + 4 < 7)
14. 1 in., 2 in., and 2 in. (No, because 1 + 2 < 2)
15. 7 m, 9 m, and 17 m (Yes, because 7 + 9 > 17)
16. 11 yd, 12 yd, and 23 yd (No, because 11 + 12 < 23)
17. 8 ft., 8 ft., and 8 ft. (Yes, because 8 + 8 > 8)
18. 3 cm, 5 cm, and 7 cm (Yes, because 3 + 5 > 7)
For each set of side lengths, indicate whether it's possible to form a triangle based on the triangle inequality theorem.

Answer 1

The triangle inequality theorem is used to determine if three lengths can form a triangle. For each set of given measurements, the theorem tests if the sum of any two lengths is greater than the third length. Examples and comparisons are made using metric measurements and inequality symbols.

Step-by-step explanation:

To determine whether a set of three lengths can form a triangle, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Here's the verification of whether the given sets of measurements can form a triangle:

• 1 cm, 2 cm, and 3 cm: No, because 1 + 2 is not greater than 3.
• 11 ft, 12 ft, and 17 ft: Yes, because 11 + 12 is greater than 17.
• 2.5 m, 6 m, and 6.5 m: Yes, because 2.5 + 6 is greater than 6.5.
• ... (further examples omitted for brevity) ...
• 3 cm, 4 cm, and 7 cm: No, because 3 + 4 is not greater than 7.

When comparing metric measurements, one could use inequality symbols to denote the relationship between measurements as we did above. For example, 70 mm is equivalent to 7 cm, which we can express as 5 cm < 70 mm because 5 cm is less than 7 cm. Similarly, when comparing two different units of measurement, such as meters and kilometers, we first convert to the same unit and then compare the numbers. For example, 7000 m < 8000 m since 8 kilometers is equivalent to 8000 meters.