Question

A three-dimensional cube with six square faces. A diagonal segment drawn on the bottom face, labeled as x.
In a cube with side length 6, what is the length of the diagonal labeled x? Round to the nearest tenth.

(1 point)
Responses

3.5
3.5

72
72

8.5
8.5

36

Answer 1

To find the length of the diagonal \( x \) on the bottom face of a cube with a side length of 6, we can use the formula for the diagonal of a square. The diagonal \( d \) of a square with side length \( s \) is given by the formula:

\[
d = s\sqrt{2}
\]

In this case, the side length \( s \) is 6. Plugging this into the formula, we get:

\[
d = 6\sqrt{2}
\]

Now we can calculate the numerical value of \( 6\sqrt{2} \):

\[
\sqrt{2} \approx 1.414
\]
\[
d \approx 6 \times 1.414 \approx 8.485
\]

Rounding this to the nearest tenth, we find:

\[
d \approx 8.5
\]

Therefore, the length of the diagonal \( x \) is:

**8.5**