https://file.aiquickdraw.com/mathbot/file/1726722860551rwgvhuyi.jpg

We are tasked with finding the length of diagonal \( \overline{AC} \) in a rectangular solid (box) with given dimensions.

### Steps to solve:
1. **Identify the dimensions**: From the image, the dimensions are:
   - Length: \( 5 \, \text{m} \)
   - Height: \( 2 \, \text{m} \)
   - Depth (from \( A \) to \( C \)): This can be inferred using the Pythagorean theorem in the base.

2. **Base diagonal (AC)**: Since \( \overline{AC} \) is a diagonal across the rectangular base of the solid, the length of \( AC \) can be found using the 3D diagonal formula:
   \[
   \text{Diagonal } = \sqrt{(\text{length})^2 + (\text{width})^2 + (\text{height})^2}
   \]

Here, the width is the unknown, but the height is known \(2

Find the length of diagonal AC in the rectangular solid shown. Dimensions are in meters.

Learn how to calculate the diagonal of a rectangular solid using the Pythagorean theorem. This geometry problem explores key concepts like the 3D diagonal formula and is ideal for students in Grades 8-10. Dimensions are given in meters.

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