Determinaţi lungimea diagonalei unui pătrat cu latura de 6 cm

The length of the diagonal of a square of length 6 cm is 6√2 cm = 8.485 cm

Step-by-step explanation:

English Translation

Determine the length of the diagonal of a square with a side of 6 cm.

Solution

Let the length of the diagonal be d.

And the length of each side of the square be s.

Note that s = 6 cm

The two sides of the square and the diagonal form a right angled triangle with the diagonal serving as the hypotenuse.

Using Pythagoras theorem, the square of the hypotenuse is equal to the sum of the individual squares of the two other sides of the right angled triangle.

d² = s² + s²

d² = 2s²

d = √(2s²)

d = s √2

note that s = 6 cm

d = 6 × √2 = 6√2 cm = 8.485 cm

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