Alisha wants to build a miniature bridge that will include a triangle made of wooden pieces. She has two wooden pieces, one of which measures 12 inches and the other of which measures 16 inches. Which could be the length of the third piece of wood in order for her to form a triangle?(1 point)
Responses
27 inches
3 inches
28 inches
4 inches
In order to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's check each possibility:
1. 27 inches: 12 + 16 > 27 (True)
2. 3 inches: 12 + 16 > 3 (True)
3. 28 inches: 12 + 16 > 28 (True)
4. 4 inches: 12 + 16 > 4 (True)
Since all four possibilities satisfy the condition, any of these lengths could be the length of the third piece of wood for Alisha to form a triangle.
To determine if a triangle can be formed with the given wooden pieces, we can apply 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 option to see if it satisfies this condition:
1. 12 inches + 16 inches > 27 inches
This is true, as 28 inches is greater than 27 inches, so a triangle can be formed.
2. 12 inches + 16 inches > 3 inches
This is false, as 28 inches is not greater than 3 inches, so a triangle cannot be formed.
3. 12 inches + 16 inches > 28 inches
This is true, as 28 inches is greater than 28 inches, so a triangle can be formed.
4. 12 inches + 16 inches > 4 inches
This is true, as 28 inches is greater than 4 inches, so a triangle can be formed.
Therefore, the only length that could be the third piece of wood for Alisha to form a triangle is 27 inches.
To determine the possible length of the third piece of wood for Alisha to 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.
In this case, Alisha has two wooden pieces measuring 12 inches and 16 inches. Let's check the possible length options:
1. 27 inches: To form a triangle, the sum of the two smaller sides must be greater than the length of the third side. However, 12 + 16 = 28, which is greater than 27. So, 27 inches could be a possible length for the third side.
2. 3 inches: Again, we need to check if the sum of the two smaller sides is greater than the length of the third side. However, 12 + 16 = 28, which is greater than 3. So, 3 inches could also be a possible length for the third side.
3. 28 inches: Similar to the previous options, if we add the two smaller sides, 12 + 16 = 28, which is already equal to the length of the third side. This means there is no room for a triangle to be formed. So, 28 inches is not a possible length for the third side.
4. 4 inches: By adding the two smaller sides, 12 + 16 = 28, which is greater than 4. So, 4 inches could be a possible length for the third side.
Considering the triangle inequality theorem, the possible length options for the third piece of wood, in order for Alisha to form a triangle, are 27 inches, 3 inches, and 4 inches.