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
A. 2
B. 11
C. 9
D. 1
Nonsense
4+6 = 10
the third side must be smaller than 10 or the ends of the 4 and 6 together will not reach the ends of more than ten.
the third side must be more than 6-4= 2 or the 4 side + the small side will not reach the ends of the 6 and 4
C, third side = 9
2 < 9 < 10
To apply the Triangle Inequality Theorem, we need to determine if the sum of any two sides of a triangle is greater than the third side.
Let's check the options:
A. 2
The sum of the first two sides (4 + 6 = 10) is greater than 2. It is possible for the third side to measure 2.
B. 11
The sum of the first two sides (4 + 6 = 10) is less than 11. It is not possible for the third side to measure 11.
C. 9
The sum of the first two sides (4 + 6 = 10) is less than 9. It is not possible for the third side to measure 9.
D. 1
The sum of the first two sides (4 + 6 = 10) is greater than 1. It is possible for the third side to measure 1.
Based on the Triangle Inequality Theorem, option A (2) and option D (1) could be the third side of a triangle.
To apply the Triangle Inequality Theorem, we need to determine if the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we have two sides measuring 4 and 6 units.
To find out if option A (2) could be the third side of the triangle, we add it to one of the given sides:
4 + 2 = 6
Since the sum (6) is equal to the other given side (6), option A would not satisfy the Triangle Inequality Theorem. Therefore, option A cannot be the third side of the triangle.
To find out if option B (11) could be the third side of the triangle, we add it to one of the given sides:
4 + 11 = 15
6 + 11 = 17
In both cases, the sums (15 and 17) are greater than the remaining side (4). Therefore, option B satisfies the Triangle Inequality Theorem and could be the third side of the triangle.
To find out if option C (9) could be the third side of the triangle, we add it to one of the given sides:
4 + 9 = 13
6 + 9 = 15
In both cases, the sums (13 and 15) are greater than the remaining side (6). Therefore, option C satisfies the Triangle Inequality Theorem and could be the third side of the triangle.
To find out if option D (1) could be the third side of the triangle, we add it to one of the given sides:
4 + 1 = 5
Since the sum (5) is smaller than the other given side (6), option D would not satisfy the Triangle Inequality Theorem. Therefore, option D cannot be the third side of the triangle.
In conclusion, options B (11) and C (9) satisfy the Triangle Inequality Theorem and could be the third side of the triangle.
According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the third side.
So, for this question:
- 4 + 6 = 10
- 10 must be greater than the third side
Looking at the options:
A. 2 is not greater than 10, so it cannot be the third side.
B. 11 is greater than 10, so it could be the third side.
C. 9 is greater than 4, but not greater than 6, so it cannot be the third side.
D. 1 is not greater than 10, so it cannot be the third side.
Therefore, option B, 11, could be the third side of a triangle if the first two sides measure 4 and 6.