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 possibilities:
1. If the length of the third piece is 27 inches, the sum of the lengths of the first two pieces (12 + 16 = 28 inches) is greater than the length of the third piece, so this could be the length of the third piece.
2. If the length of the third piece is 3 inches, the sum of the lengths of the first two pieces (12 + 16 = 28 inches) is greater than the length of the third piece, so this could be the length of the third piece.
3. If the length of the third piece is 28 inches, the sum of the lengths of the first two pieces (12 + 16 = 28 inches) is equal to the length of the third piece. In this case, the pieces are on the same line and cannot form a triangle, so this cannot be the length of the third piece.
4. If the length of the third piece is 4 inches, the sum of the lengths of the first two pieces (12 + 16 = 28 inches) is greater than the length of the third piece, so this could be the length of the third piece.
Therefore, the possible lengths for the third piece of wood in order to form a triangle are 27 inches, 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 27 inches 27 inches 3 inches 3 inches 28 inches 28 inches 4 inches
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