To determine the length of the third side of a triangle, we can use the triangle inequality theorem. According to this 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 sum of the lengths of the first two sides (10 and 12) is 22. So, the length of the third side must be less than 22 for a valid triangle.
Therefore, the correct choice is 15.
Question
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
30
30
15
15
22
22
24
7 answers
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
10 cm
10 cm
6 cm
6 cm
5 cm
5 cm
8 cm
Responses
10 cm
10 cm
6 cm
6 cm
5 cm
5 cm
8 cm
To determine which of the following choices cannot be the measure of the third side of a triangle with sides measuring 4 cm and 9 cm, we can use the triangle inequality theorem. According to this 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 sum of the lengths of the first two sides (4 cm and 9 cm) is 13 cm. So, the length of the third side must be less than 13 cm for a valid triangle.
Therefore, the correct choice is 10 cm because it is greater than 13 cm.
In this case, the sum of the lengths of the first two sides (4 cm and 9 cm) is 13 cm. So, the length of the third side must be less than 13 cm for a valid triangle.
Therefore, the correct choice is 10 cm because it is greater than 13 cm.
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
2
2
11
11
9
9
1
Responses
2
2
11
11
9
9
1
To determine which option could be the third side of a triangle with sides measuring 4 and 6, we can use the triangle inequality theorem. According to this 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 sum of the lengths of the first two sides (4 and 6) is 10. The length of the third side must be less than 10 cm for a valid triangle.
Therefore, the correct choice is 9 because it is less than 10 cm.
In this case, the sum of the lengths of the first two sides (4 and 6) is 10. The length of the third side must be less than 10 cm for a valid triangle.
Therefore, the correct choice is 9 because it is less than 10 cm.
Question
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
2, 7, 6
2, 7, 6
9, 4, 3
9, 4, 3
12, 10, 22
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
2, 7, 6
2, 7, 6
9, 4, 3
9, 4, 3
12, 10, 22
To determine which group of side measures will form a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each group of side measures:
1) 8, 1, 7:
The sum of the two smaller sides (1 and 7) is 8. However, this is not greater than the longest side (8). Therefore, this group of side measures will not form a triangle.
2) 2, 7, 6:
The sum of the two smaller sides (2 and 6) is 8, which is equal to the longest side (7). Therefore, this group of side measures forms a degenerate triangle, which is a line segment.
3) 9, 4, 3:
The sum of the two smaller sides (3 and 4) is 7, which is greater than the longest side (9). Therefore, this group of side measures will form a triangle.
4) 12, 10, 22:
The sum of the two smaller sides (10 and 12) is 22, which is equal to the longest side (22). Therefore, this group of side measures forms a degenerate triangle, which is a line segment.
Thus, the group of side measures that will form a triangle is 9, 4, 3.
Let's check each group of side measures:
1) 8, 1, 7:
The sum of the two smaller sides (1 and 7) is 8. However, this is not greater than the longest side (8). Therefore, this group of side measures will not form a triangle.
2) 2, 7, 6:
The sum of the two smaller sides (2 and 6) is 8, which is equal to the longest side (7). Therefore, this group of side measures forms a degenerate triangle, which is a line segment.
3) 9, 4, 3:
The sum of the two smaller sides (3 and 4) is 7, which is greater than the longest side (9). Therefore, this group of side measures will form a triangle.
4) 12, 10, 22:
The sum of the two smaller sides (10 and 12) is 22, which is equal to the longest side (22). Therefore, this group of side measures forms a degenerate triangle, which is a line segment.
Thus, the group of side measures that will form a triangle is 9, 4, 3.
5 answers