Final answer:
The length of the diagonal of a square with sides measuring 10 cm is found using the Pythagorean theorem, which gives an approximate value of 14.14 cm.
Step-by-step explanation:
To calculate the length of the diagonal of a square with sides that measure 10 cm each, you can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. As the diagonal of a square forms two right-angled triangles, we can use the theorem to make a formula for the diagonal (d):
d = √(side² + side²).
For a side length of 10 cm, this becomes:
d = √(10 cm² + 10 cm²)
= √(100 cm² + 100 cm²)
= √200 cm²
= approximately 14.14 cm.
So, the diagonal of the square measures approximately 14.14 cm.