Final answer:
Using the Pythagorean theorem, it is calculated that the value of c is 13 cm when a is 12 cm and b is 5 cm, answering the student's question with option c).
Step-by-step explanation:
To find the value of c when a = 12 cm and b = 5 cm, we can use the Pythagorean theorem if we assume that the question pertains to a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The formula is c² = a² + b². Plugging in the given values:
- c² = (12 cm)² + (5 cm)²
- c² = 144 cm² + 25 cm²
- c² = 169 cm²
- c = √169 cm²
- c = 13 cm
Therefore, the value of c is 13 cm, which corresponds to option c).