Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.(1 point)
Responses
15
24
22
30
To determine the length of the third side of a triangle, you can 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.
In this case, the first two sides measure 10 and 12. Let's test the lengths provided in the choices to see which one satisfies the triangle inequality theorem.
1) 15: 10 + 12 = 22, which is not greater than 15. This choice does not satisfy the triangle inequality theorem.
2) 24: 10 + 12 = 22, which is not greater than 24. This choice does not satisfy the triangle inequality theorem.
3) 22: 10 + 12 = 22, which is equal to 22. This choice does not satisfy the triangle inequality theorem.
4) 30: 10 + 12 = 22, which is less than 30. This choice satisfies the triangle inequality theorem.
Therefore, the length of the third side of the triangle is 30.
Two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.(1 point)
Responses
5 cm
5 cm
6 cm
6 cm
8 cm
8 cm
10 cm
10 cm
To determine which of the following choices cannot be the measure of the third side of a triangle, we can use the triangle inequality theorem. The 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.
In this case, the given sides measure 4 cm and 9 cm. Let's test the lengths provided in the choices to see which one satisfies the triangle inequality theorem.
1) 5 cm: 4 + 5 = 9, which is equal to 9. This choice satisfies the triangle inequality theorem.
2) 6 cm: 4 + 6 = 10, which is greater than 9. This choice satisfies the triangle inequality theorem.
3) 8 cm: 4 + 8 = 12, which is greater than 9. This choice satisfies the triangle inequality theorem.
4) 10 cm: 4 + 10 = 14, which is greater than 9. This choice satisfies the triangle inequality theorem.
Therefore, all of the choices provided can be the measure of the third side of the triangle.
only one so pick the right one
Apologies for the confusion. Based on the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the given sides measure 4 cm and 9 cm. Let's test the lengths provided in the choices to see which one does not satisfy the triangle inequality theorem.
1) 5 cm: 4 + 5 = 9, which is equal to 9. This choice satisfies the triangle inequality theorem.
2) 6 cm: 4 + 6 = 10, which is greater than 9. This choice satisfies the triangle inequality theorem.
3) 8 cm: 4 + 8 = 12, which is greater than 9. This choice satisfies the triangle inequality theorem.
4) 10 cm: 4 + 10 = 14, which is greater than 9. This choice satisfies the triangle inequality theorem.
Therefore, all of the choices provided satisfy the triangle inequality theorem, and none of them cannot be the measure of the third side of the triangle.
choose the best on please
Apologies for the confusion. Based on the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the given sides measure 4 cm and 9 cm. Let's test the lengths provided in the choices to see which one does not satisfy the triangle inequality theorem.
1) 5 cm: 4 + 5 = 9, which is equal to 9. This choice satisfies the triangle inequality theorem.
2) 6 cm: 4 + 6 = 10, which is greater than 9. This choice satisfies the triangle inequality theorem.
3) 8 cm: 4 + 8 = 12, which is greater than 9. This choice satisfies the triangle inequality theorem.
4) 10 cm: 4 + 10 = 14, which is greater than 9. This choice satisfies the triangle inequality theorem.
Based on the triangle inequality theorem, all of the choices provided can be the measure of the third side of the triangle. Therefore, none of the choices provided cannot be the measure of the third side.
Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point)
Responses
11
2
9
1
To apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle, we need to check if the sum of the two given sides is greater than the length of the third side.
The given sides measure 4 and 6.
1) Option 11: 4 + 6 = 10, which is less than 11. This option satisfies the Triangle Inequality Theorem.
2) Option 2: 4 + 6 = 10, which is greater than 2. This option also satisfies the Triangle Inequality Theorem.
3) Option 9: 4 + 6 = 10, which is less than 9. This option does not satisfy the Triangle Inequality Theorem.
4) Option 1: 4 + 6 = 10, which is greater than 1. This option satisfies the Triangle Inequality Theorem.
Based on the Triangle Inequality Theorem, the only option that could be the third side of a triangle is 1.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point)
Responses
12, 10, 22
12, 10, 22
8, 1, 7
8, 1, 7
9, 4, 3
9, 4, 3
2, 7, 6
2, 7, 6