Final answer:
The range of possible values for the length of the third side of a triangle with two sides measuring 7 cm each is greater than 0 cm and less than 14 cm. According to the triangle inequality theorem, the third side must be greater than the difference and less than the sum of the two equal sides. The correct answer is therefore option (A): 1 cm ≤ Third side < 14 cm.
Step-by-step explanation:
The question asks what is the range of possible values for the length of the third side of a triangle if the lengths of two sides are 7 cm each. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. At the same time, the difference of the lengths of any two sides of a triangle must be less than the length of the third side.
To find the minimum length of the third side, we subtract one of the sides from the other (though they are equal in this case): 7 cm - 7 cm = 0 cm. However, since we can't have a side of zero length, we must conclude that the third side must be greater than 0 cm. Therefore, the minimum length is anything greater than 0 cm, which we can state as the third side must be greater than 0 cm.
To find the maximum length of the third side, we add the lengths of the two sides: 7 cm + 7 cm = 14 cm. The third side must be less than this sum, so the maximum length is anything less than 14 cm.
Therefore, the correct range of possible values for the length of the third side is > 0 cm and < 14 cm, which matches the option (A): 1 cm ≤ Third side < 14 cm. The correct answer is option (A), not (D), which was the answer provided by the student.