To find the ratio of the corresponding side lengths of the two rectangles given the ratio of their areas, we can start by denoting the areas of the rectangles as \( A_1 \) and \( A_2 \). We know that the ratio of the areas is given by:
\[ \frac{A_1}{A_2} = \frac{16}{25} \]
Let the side lengths of the first and second rectangles be denoted by \( l_1 \) and \( l_2 \) for one dimension, and \( w_1 \) and \( w_2 \) for the other dimension. Thus, the areas can be expressed as:
\[ A_1 = l_1 \cdot w_1 \quad \text{and} \quad A_2 = l_2 \cdot w_2 \]
From the ratio of the areas, we can also express the ratio as follows:
\[ \frac{A_1}{A_2} = \frac{l_1 \cdot w_1}{l_2 \cdot w_2} \]
We can then rewrite the ratio of the side lengths as:
\[ \frac{l_1}{l_2} \cdot \frac{w_1}{w_2} = \frac{16}{25} \]
Let the ratio of the corresponding side lengths of the rectangles be:
\[ \frac{l_1}{l_2} = x \quad \text{and} \quad \frac{w_1}{w_2} = y \]
From the equation above, we have:
\[ x \cdot y = \frac{16}{25} \]
Next, since the ratio of the areas is a square of the ratio of the corresponding side lengths, we can use the following relationship:
\[ \left(\frac{l_1}{l_2}\right)^2 = \frac{A_1}{A_2} \]
This implies:
\[ \left(\frac{l_1}{l_2}\right)^2 = \frac{16}{25} \]
Taking the square root of both sides gives us:
\[ \frac{l_1}{l_2} = \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5} \]
Thus, the ratio of the corresponding side lengths of the two rectangles in simplest form is:
\[ \frac{4}{5} \]
So, the final answer is:
\[ \boxed{\frac{4}{5}} \]
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