Question

what is the length of the diagonal of this square?
type your answer in the box.
units

Explanation:

Step1: Identify side length

The square has side length \( s = 1 \) unit (from the diagram, all sides are equal and marked with length 1).

Step2: Apply Pythagorean theorem

For a square, the diagonal \( d \) forms a right triangle with two sides. Using the Pythagorean theorem \( d^{2}=s^{2}+s^{2} \). Substituting \( s = 1 \), we get \( d^{2}=1^{2}+1^{2}=1 + 1=2 \). Then, \( d=\sqrt{2} \) (since length is positive, we take the positive square root).

Answer:

\(\sqrt{2}\)