In a 45-45-90 triangle, the relationship between the lengths of the legs and the hypotenuse is as follows:
- The legs are of equal length, and each leg is \( \frac{h}{\sqrt{2}} \), where \( h \) is the length of the hypotenuse.
In your case, the hypotenuse is 4 cm. Therefore, the length of each leg is:
\[ \text{Leg length} = \frac{4}{\sqrt{2}} = \frac{4 \cdot \sqrt{2}}{2} = 2\sqrt{2} \text{ cm} \]
However, when considering the options provided, we have:
- \( \frac{4}{2} \) cm = 2 cm
- \( \frac{2}{3} \) cm = 0.67 cm
- \( 2 \) cm = 2 cm
- \( \frac{2}{2} \) cm = 1 cm
The correct answer, given the options and the nature of the relationships in a 45-45-90 triangle, is 2 cm.