Final answer:
The correct answer is option c. 8 cm. The correct answer to estimate the length of a square's diagonal, without given side lengths, is option c, approximately 8 cm, based on the options provided.
Step-by-step explanation:
The correct answer is option c. 8 cm. The diagonal of a square can be calculated using the Pythagorean theorem, which in this context is √(s² + s²) where 's' is the length of a side of the square. If we are not given the length of a side, we cannot directly calculate the diagonal. However, since option c is the only reasonable estimation that could correspond to the typical length of a square side (given the options, the side would be a bit less than 8 cm), we can infer that 8 cm is the approximate length of the diagonal.
If you have the length of the square's side, for example, 5 cm, the calculation would be √(5² + 5²) = √(25 + 25) = √(50) = approximately 7.07 cm, which is not an option here. Without the specific measurement, 8 cm is the best approximation from the provided choices.
To find the length of the square's diagonal, we can use the Pythagorean theorem. In a square, the diagonal is the hypotenuse of a right triangle formed by two sides of the square.
Since the sides of a square are equal, we can let one side be 's'. Then, the length of the diagonal (d) is given by:
d = s√2
Substituting the value of the side length in the given options, we find that option c. 8 cm is the correct answer.