Final answer:
To find the third side of a triangle when the perimeter is known, subtract the total length of the two known sides from the perimeter. The student's answer of 4 cm for the third side is correct if the other two sides indeed add up to 14 cm (18 - 4 = 14). More information about the specific side lengths is needed for a tailored solution.
Explanation:
To solve for the measure of the third side of a triangle when the perimeter is known and two sides are given, we can use the formula for the perimeter of a triangle, which is the sum of the lengths of all three sides. The formula can be represented as P = a + b + c, where P represents the perimeter, and a, b, and c represent the lengths of the sides of the triangle.
Given that the perimeter (P) is 18 cm and you have two of the side lengths, let's say a and b, you would subtract the sum of these two sides from the total perimeter to find the length of the third side (c). Let's represent the two known sides as a and b; then the formula becomes c = P - (a + b).
However, the values for a and b are not given in the provided information. Given the correct values for sides a and b, you would substitute them into the equation to find the length of side c. As your answer is that the third side measures 4 cm, we would expect the other two sides to have a combined length of 14 cm (since 18 - 4 = 14). If this is the case, then your answer of 4 cm for the third side is correct.
If more data were provided about the measurements of sides a and b, or the specific angles involved, we could provide a more tailored solution.