Final answer:
The diagonal length of a square with a side length of 10 cm is 10√2 cm, which is approximately 14.14 cm.
Step-by-step explanation:
The diagonal length of a square with a side length of 10 cm can be calculated using the Pythagorean theorem. Since a square has all sides equal, we can say that both the width and the height of the square are 10 cm. The diagonal creates a right-angled triangle with the sides of the square. According to the Pythagorean theorem (c² = a² + b²), where c is the diagonal, and a and b are the sides of the square:
- c² = 10² + 10²
- c² = 100 + 100
- c² = 200
- c = √200
- c = √(100 × 2)
- c = √100 × √2
- c = 10√2
Hence, the diagonal length of the square is 10√2 cm, which is approximately 14.14 cm when √2 is approximated to 1.414.