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The problem shows two similar rectangular prisms. To find the value of \( y \), we use the fact that for similar figures, the corresponding side lengths are proportional. Let's define the sides of the prisms based on the labels given.

For the larger prism:
- One side = 8 inches,
- Another side = 12 inches,
- Another side = 3 inches.

For the smaller prism:
- One side = \( y \) inches (corresponds to 8 inches of the larger prism),
- One side = \( q \) inches (corresponds to 12 inches of the larger prism),
- One side = \( x \) inches (corresponds to 3 inches of the larger prism).

The ratio of corresponding sides must be equal. Let's set up a proportion using the dimensions where we know the values from both prisms.

\[
\frac{8 \, \text{in}}{y \, \text{in}} = \frac{12 \, \text{in}}{q \, \text{in}} = \frac{3 \, \text{in}}{x \, \text{in}}
\]

To solve for \( y \), we need the ratio \( \frac{8}{y} = \frac{3}{x} \). Once we know \( x \), we can directly solve for \( y \).

Do you have the value of \( x \), or should I assume a missing proportion to solve for \( y \)? Let me know!

The rectangular prisms shown below are similar. What is the value of y?

This problem involves finding the value of y by applying proportionality in similar rectangular prisms. The corresponding side ratios must be equal, and we use this relationship to solve for the missing value y. Suitable for students in Grades 7-9.

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