To solve for the hypotenuse of the second triangle, we first recognize that both triangles are isosceles right triangles (45-45-90 triangles). In such triangles, the relationships between the lengths of the sides and the hypotenuse are consistent: if the legs (the two sides opposite the 45° angles) have length \( x \), the hypotenuse \( h \) is given by
\[ h = x \sqrt{2}. \]
Now, we analyze the second triangle:
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Identifying the leg length: The length of the side opposite the 45° angle in the second triangle is \( 4 \sqrt{2} \).
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Calculating the hypotenuse: Since the length of each leg in a 45-45-90 triangle is equal, we can identify the leg length \( x \) as \( 4 \sqrt{2} \).
To find the hypotenuse \( h \), we apply the formula:
\[ h = x \sqrt{2}. \] Substituting \( x = 4 \sqrt{2} \):
\[ h = (4 \sqrt{2}) \sqrt{2}. \]
Using the property of square roots \( \sqrt{2} \cdot \sqrt{2} = 2 \), we simplify this as:
\[ h = 4 \cdot 2 = 8. \]
Thus, the length of the hypotenuse in the second triangle is
\[ \boxed{8}. \]
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