According to the Triangle Inequality Theorem, a triangle can only be formed if the sum of the lengths of any two sides is greater than the length of the third side.
Using this theorem, we can check each group of side measures:
1) 8 + 1 = 9; 9 > 7. Additionally, 8 + 7 = 15; 15 > 1. Lastly, 1 + 7 = 8; 8 > 8. Therefore, the group of side measures 8, 1, and 7 will form a triangle.
2) 12 + 10 = 22; 22 = 22. In this case, the sum of any two sides is equal to the length of the third side. According to the Triangle Inequality Theorem, a triangle can only be formed if the sum of the lengths of any two sides is greater than the length of the third side. Therefore, the group of side measures 12, 10, and 22 will not form a triangle.
3) 2 + 7 = 9; 9 > 6. Additionally, 2 + 6 = 8; 8 > 7. Lastly, 7 + 6 = 13; 13 > 2. Therefore, the group of side measures 2, 7, and 6 will form a triangle.
4) 9 + 4 = 13; 13 > 3. Additionally, 9 + 3 = 12; 12 > 4. Lastly, 4 + 3 = 7; 7 > 9. Therefore, the group of side measures 9, 4, and 3 will form a triangle.
In conclusion, the groups of side measures that will form a triangle are:
- 8, 1, 7
- 2, 7, 6
- 9, 4, 3
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses
8, 1, 7
8, 1, 7
12, 10, 22
12, 10, 22
2, 7, 6
2, 7, 6
9, 4, 3
7 answers
A B C or d
The correct response is:
D. 9, 4, 3
D. 9, 4, 3
Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side.(1 point)
Responses
4.5
4.5
5.5
5.5
4.2
4.2
3.5
Responses
4.5
4.5
5.5
5.5
4.2
4.2
3.5
According to the Triangle Inequality Theorem, a triangle can only be formed if the sum of the lengths of any two sides is greater than the length of the third side.
In this case, we have side lengths of 3.7 and 8.2. Let's check the possible measures of the third side:
1) 3.7 + 8.2 = 11.9; 11.9 > 4.5. Therefore, a possible measure of the third side is 4.5.
2) 3.7 + 8.2 = 11.9; 11.9 > 5.5. Therefore, a possible measure of the third side is 5.5.
3) 3.7 + 8.2 = 11.9; 11.9 > 4.2. Therefore, a possible measure of the third side is 4.2.
4) 3.7 + 8.2 = 11.9; 11.9 > 3.5. Therefore, a possible measure of the third side is 3.5.
Therefore, all of the given measurements (4.5, 5.5, 4.2, and 3.5) are possible measures for the third side of the triangle.
In this case, we have side lengths of 3.7 and 8.2. Let's check the possible measures of the third side:
1) 3.7 + 8.2 = 11.9; 11.9 > 4.5. Therefore, a possible measure of the third side is 4.5.
2) 3.7 + 8.2 = 11.9; 11.9 > 5.5. Therefore, a possible measure of the third side is 5.5.
3) 3.7 + 8.2 = 11.9; 11.9 > 4.2. Therefore, a possible measure of the third side is 4.2.
4) 3.7 + 8.2 = 11.9; 11.9 > 3.5. Therefore, a possible measure of the third side is 3.5.
Therefore, all of the given measurements (4.5, 5.5, 4.2, and 3.5) are possible measures for the third side of the triangle.
abc or d
The correct response is:
B. 5.5
B. 5.5
1 answer