In a 45-45-90 triangle, the relationship between the lengths of the legs and the hypotenuse can be derived from the properties of a 45-45-90 triangle.
The lengths of the legs (let's call them \( x \)) are related to the hypotenuse (let's call it \( h \)) by the formula:
\[ h = x\sqrt{2} \]
In this case, the hypotenuse given is 4 cm:
\[ 4 = x\sqrt{2} \]
To find the length of the leg, \( x \), we can solve for \( x \):
\[ x = \frac{4}{\sqrt{2}} \]
To simplify \( x \):
\[ x = \frac{4\sqrt{2}}{2} = 2\sqrt{2} \text{ cm} \]
Thus, the length of each leg of the triangle is \( 2\sqrt{2} \) cm.
The correct response is: 2√2 cm