In a 45-45-90 triangle, the lengths of the legs are equal, and the relationship between the length of the legs (let's call it \( x \)) and the length of the hypotenuse \( h \) can be expressed as:
\[ h = x\sqrt{2} \]
Given that the hypotenuse \( h \) is 4 cm, we can set up the equation:
\[ 4 = x\sqrt{2} \]
To find \( x \), we can solve for it:
\[ x = \frac{4}{\sqrt{2}} \]
To simplify \( x \), we can multiply the numerator and denominator by \( \sqrt{2} \):
\[ x = \frac{4\sqrt{2}}{2} = 2\sqrt{2} \]
Thus, the length of each leg is \( 2\sqrt{2} \) cm. Therefore, the correct response is:
\( 2\sqrt{2} , \text{cm} \).