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
27 inches
3 inches
3 inches
28 inches
28 inches
4 inches
In order to form a triangle, the length of the third side must be greater than the difference between the lengths of the other two sides and less than their sum. Let's check the options:
1. 27 inches: 12 + 16 = 28 (greater than 27), and 16 - 12 = 4 (less than 27). Therefore, 27 inches is within the range.
2. 3 inches: 12 + 16 = 28 (greater than 3), and 16 - 12 = 4 (less than 3). Therefore, 3 inches is outside the range.
3. 28 inches: 12 + 16 = 28 (equal to 28), and 16 - 12 = 4 (greater than 28). Therefore, 28 inches is outside the range.
4. 4 inches: 12 + 16 = 28 (greater than 4), and 16 - 12 = 4 (less than 4). Therefore, 4 inches is within the range.
Therefore, the correct answer is 27 inches.
The length of the third piece of wood must be less than the sum of the lengths of the other two pieces and greater than the difference between the lengths of the other two pieces.
In this case, the sum of the lengths of the other two pieces is 12 + 16 = 28 inches. Therefore, the third piece of wood cannot be 27 inches or 28 inches, as these lengths are greater than the sum of the other two pieces.
The difference between the lengths of the other two pieces is 16 - 12 = 4 inches. Therefore, the third piece of wood cannot be 3 inches or 4 inches, as these lengths are smaller than the difference between the other two pieces.
Therefore, none of the given options are a possible length for the third piece of wood to form a triangle.