1. The three side lengths that form a triangle using the Triangle Inequality Theorem are:
- 7, 8, 9
- 7, 5, 13
2. False, the measurements of 3 ft., 4 ft., and 6 ft. will not form a triangle.
3. A possible length of the 3rd side of a triangle with two sides measuring 5 in. and 13 in. is:
- 6 in.
Use the Triangle Inequality Theorem to determine which three side lengths form a triangle. *
1 point
2, 7, 9
7, 8, 9
7, 5, 13
4, 15, 20
Truer False:
The measurements of 3 ft., 4ft., and 6 ft. will form a triangle?
*
1 point
True
False
Two sides of a triangle are 5 in. and 13in. What is a possible length of the 3rd side? *
2 points
3 in.
5 in.
6 in.
9 in.
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3 answers
can u explain for all of them?
Sure!
1. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, applying the theorem to the sets of side lengths given:
- For 2, 7, 9: 2 + 7 = 9, which is equal to the third side, so they do not form a triangle.
- For 7, 8, 9: 7 + 8 = 15, which is greater than 9. Likewise, 7 + 9 = 16, which is greater than 8. Also, 8 + 9 = 17, which is greater than 7. Therefore, the sides 7, 8, and 9 form a triangle.
- For 7, 5, 13: 7 + 5 = 12, which is less than 13. Also, 7 + 13 = 20, which is greater than 5. Finally, 5 + 13 = 18, which is greater than 7. Therefore, the sides 7, 5, and 13 form a triangle.
2. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the case of 3 ft., 4 ft., and 6 ft., the sum of 3 ft. + 4 ft. is 7 ft., which is less than 6 ft. Therefore, these side lengths will not form a triangle.
3. For a triangle with side lengths of 5 in. and 13 in., the third side must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, a possible length for the third side of this triangle would be 6 in., as 5 in. + 6 in. = 11 in. and 13 in. > 11 in., satisfying the theorem.
1. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, applying the theorem to the sets of side lengths given:
- For 2, 7, 9: 2 + 7 = 9, which is equal to the third side, so they do not form a triangle.
- For 7, 8, 9: 7 + 8 = 15, which is greater than 9. Likewise, 7 + 9 = 16, which is greater than 8. Also, 8 + 9 = 17, which is greater than 7. Therefore, the sides 7, 8, and 9 form a triangle.
- For 7, 5, 13: 7 + 5 = 12, which is less than 13. Also, 7 + 13 = 20, which is greater than 5. Finally, 5 + 13 = 18, which is greater than 7. Therefore, the sides 7, 5, and 13 form a triangle.
2. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the case of 3 ft., 4 ft., and 6 ft., the sum of 3 ft. + 4 ft. is 7 ft., which is less than 6 ft. Therefore, these side lengths will not form a triangle.
3. For a triangle with side lengths of 5 in. and 13 in., the third side must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, a possible length for the third side of this triangle would be 6 in., as 5 in. + 6 in. = 11 in. and 13 in. > 11 in., satisfying the theorem.
1 answer