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What is the diagonal iength of a square that has a side length of 10cm ?

User Raimon
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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.

User Gnome
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