Final answer:
The sides of a square with an area of 121 cm² are 11 cm long. The diagonal of this square is approximately 15.56 cm, calculated using the Pythagorean theorem for a square's diagonal.
Step-by-step explanation:
If the area of a square is 121 cm², we find the length of the sides by taking the square root of the area, as the area of a square is given by side length squared (s²).
Therefore, the side length (s) is the square root of 121 cm², which is 11 cm. This is because 11 cm × 11 cm gives us 121 cm².
To find the diagonal of the square, we can use the Pythagorean theorem because the diagonal splits the square into two right-angled triangles. For a square, the diagonal (d) is given by d = s√2. So the diagonal length would be 11 cm × √2 ≈ 15.56 cm.