Which set of side lengths will form a triangle? All lengths are given in meters.(1 point)
Responses
50, 30, 80
26, 12, 12
50, 60, 26
60, 26, 33
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's check each set of side lengths:
1) 50 + 30 = 80, which is greater than 80. However, 50 + 80 = 130, which is not greater than 30. Therefore, this set of side lengths (50, 30, 80) will not form a triangle.
2) 26 + 12 = 38, which is greater than 12. However, 12 + 12 = 24, which is not greater than 26. Therefore, this set of side lengths (26, 12, 12) will not form a triangle.
3) 50 + 60 = 110, which is greater than 26. Additionally, 60 + 26 = 86, which is greater than 50. Lastly, 26 + 50 = 76, which is greater than 60. Therefore, this set of side lengths (50, 60, 26) will form a triangle.
4) 60 + 26 = 86, which is greater than 33. Additionally, 26 + 33 = 59, which is greater than 60. Lastly, 33 + 60 = 93, which is greater than 26. Therefore, this set of side lengths (60, 26, 33) will form a triangle.
So, the set of side lengths that will form a triangle is (50, 60, 26).
To determine which set of side lengths will form a triangle, we 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 remaining side.
Let's check each set of side lengths:
1) 50, 30, 80
The sum of the first two sides is 50 + 30 = 80, which is equal to the third side. This does not satisfy the triangle inequality theorem, so this set of side lengths will not form a triangle.
2) 26, 12, 12
The sum of the first two sides is 26 + 12 = 38, which is greater than the third side. Also, the sum of the last two sides is 12 + 12 = 24, which is greater than the first side. This set of side lengths satisfies the triangle inequality theorem, so it will form a triangle.
3) 50, 60, 26
The sum of the first two sides is 50 + 60 = 110, which is greater than the third side. Also, the sum of the last two sides is 60 + 26 = 86, which is greater than the first side. This set of side lengths satisfies the triangle inequality theorem and will form a triangle.
4) 60, 26, 33
The sum of the first two sides is 60 + 26 = 86, which is greater than the third side. Also, the sum of the last two sides is 26 + 33 = 59, which is greater than the first side. This set of side lengths satisfies the triangle inequality theorem and will form a triangle.
Therefore, the sets of side lengths that will form a triangle are:
- 26, 12, 12
- 50, 60, 26
- 60, 26, 33