In a 45-45-90 triangle, the lengths of the legs are equal, and the relationship between the lengths of the legs and the hypotenuse is given by the formula:
\[ \text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} \]
Given that the hypotenuse is 4 cm, we can substitute this value into the formula:
\[ \text{Leg} = \frac{4}{\sqrt{2}} \]
To simplify \(\frac{4}{\sqrt{2}}\), we can multiply the numerator and the denominator by \(\sqrt{2}\):
\[ \text{Leg} = \frac{4 \sqrt{2}}{2} = 2 \sqrt{2} \text{ cm} \]
So, the length of each leg in the triangle is \(2\sqrt{2}\) cm.
The correct response is: 2√2 cm