https://file.aiquickdraw.com/mathbot/file/1729696889003omyypb7m.jpg

The diagram in the image shows a cuboid with dimensions 8 cm, 6 cm, and 10 cm. We are asked to find the length of the diagonal \( x \) (across the face of the cuboid) from one corner of the cuboid to the opposite corner on the front face.

### Step-by-Step Solution:

1. **Diagonal on the base (bottom rectangle)**:
   - The base of the cuboid is a rectangle with dimensions 8 cm and 6 cm.
   - Using the Pythagorean theorem, the diagonal \( d \) of this base is:
   \[
   d = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{cm}
   \]

2. **Diagonal of the cuboid**:
   - Now, we use the Pythagorean theorem again to find \( x \), the diagonal from the top back corner to the bottom front corner of the cuboid. This diagonal runs through the height (10 cm) and the base diagonal (which we just calculated as 10 cm):
   \[
   x = \sqrt{10^2 + 10^2} = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \, \text{cm} \approx 14.14 \, \text{cm}
   \]

Thus, the value of \( x \) is approximately **14.14 cm**.

Would you like more details or have any questions about the solution?

Here are 5 related questions you might want to explore:
1. How can you calculate the surface area of this cuboid?
2. What is the volume of the cuboid?
3. How would you find the total length of all edges of the cuboid?
4. Can you calculate the space diagonal of a cube instead of a cuboid?
5. How does the Pythagorean theorem apply to three-dimensional shapes?

**Tip:** When solving 3D geometry problems involving diagonals, always remember to apply the Pythagorean theorem in two steps—first within one plane, then using the result for the third dimension.

Determine the value of x in the cuboid with dimensions 8 cm, 6 cm, and 10 cm.

This problem demonstrates how to calculate the diagonal of a cuboid using the Pythagorean theorem. Given dimensions are 8 cm, 6 cm, and 10 cm. Learn the step-by-step solution, involving both the base diagonal and the full cuboid diagonal.

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