https://file.aiquickdraw.com/mathbot/file/1730011905979ocm21bae.jpg

To find the diagonal \( x \) of the cuboid, we can use the 3D Pythagorean theorem. For a cuboid with side lengths \( a \), \( b \), and \( c \), the space diagonal \( x \) is given by:

\[
x = \sqrt{a^2 + b^2 + c^2}
\]

From the image:
- \( a = 7.8 \, \text{cm} \)
- \( b = 5.6 \, \text{cm} \)
- \( c = 4.4 \, \text{cm} \)

Substituting these values:

\[
x = \sqrt{(7.8)^2 + (5.6)^2 + (4.4)^2}
\]

Calculating each term:
- \( (7.8)^2 = 60.84 \)
- \( (5.6)^2 = 31.36 \)
- \( (4.4)^2 = 19.36 \)

Adding these up:

\[
x = \sqrt{60.84 + 31.36 + 19.36} = \sqrt{111.56}
\]

Now, taking the square root:

\[
x \approx 10.56 \, \text{cm}
\]

So, \( x \approx 10.6 \, \text{cm} \) (rounded to one decimal place).

### Answer:
\[
x = 10.6 \, \text{cm}
\]

Would you like more details on any steps, or have further questions?

### Related Questions:
1. What is the formula for the diagonal of a cuboid with different dimensions?
2. How would the calculation change if one of the side lengths doubled?
3. What is the surface area of this cuboid?
4. How can we calculate the volume of this cuboid?
5. If this cuboid were hollow, how would we find the thickness given an inner and outer dimension?

### Tip:
For three-dimensional problems, the Pythagorean theorem can extend to find lengths across multiple dimensions by adding squared values of each spatial component.

x is the diagonal of a cuboid with side lengths 7.8 cm, 5.6 cm, and 4.4 cm. Find x.

Learn how to find the space diagonal of a cuboid with side lengths of 7.8 cm, 5.6 cm, and 4.4 cm. This problem applies the 3D Pythagorean theorem to calculate the diagonal, suitable for Grades 9-10 geometry students.

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