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 consider the options given:
1) If the third piece of wood is 3 inches, the sum of the lengths of the other two sides would be 12 + 16 = 28 inches, which is greater than 3 inches. Therefore, this is a possible length for the third piece of wood in order to form a triangle.
2) If the third piece of wood is 27 inches, the sum of the lengths of the other two sides would be 12 + 16 = 28 inches, which is equal to 27 inches. In this case, the two shorter sides would form a straight line, and a triangle cannot be formed. Therefore, this is not a possible length for the third piece of wood.
3) If the third piece of wood is 28 inches, the sum of the lengths of the other two sides would be 12 + 16 = 28 inches, which is equal to 28 inches. In this case, the two shorter sides would form a straight line, and a triangle cannot be formed. Therefore, this is not a possible length for the third piece of wood.
4) If the third piece of wood is 4 inches, the sum of the lengths of the other two sides would be 12 + 16 = 28 inches, which is greater than 4 inches. Therefore, this is a possible length for the third piece of wood in order to form a triangle.
So, the possible lengths for the third piece of wood in order to form a triangle are 3 inches and 4 inches. Hence, the correct response is 3 inches and 4 inches.
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
3 inches
27 inches
28 inches
4 inches
1 answer