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 14, what is the length of the diagonal labeled x? Round to the nearest tenth.

(1 point)
Responses

5.3
5.3

3.7
3.7

28
28

19.8

Answer 1

To find the length of the diagonal \( x \) on the bottom face of a cube with a side length of 14, we can use the Pythagorean theorem. In a square, the diagonal can be calculated as follows:

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

where \( s \) is the side length of the square. For this cube:

\[
s = 14
\]

Plugging in the value:

\[
d = \sqrt{14^2 + 14^2} = \sqrt{196 + 196} = \sqrt{392}
\]

Now, calculating \( \sqrt{392} \):

\[
\sqrt{392} = \sqrt{4 \times 98} = \sqrt{4} \times \sqrt{98} = 2 \times \sqrt{98}
\]
\[
\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}
\]

Thus:

\[
d = 2 \times 7\sqrt{2} = 14\sqrt{2}
\]

Next, we find the approximate value of \( \sqrt{2} \):

\[
\sqrt{2} \approx 1.414
\]

Now, substituting back to find \( d \):

\[
d \approx 14 \times 1.414 \approx 19.796
\]

Rounding 19.796 to the nearest tenth gives us:

\[
d \approx 19.8
\]

Therefore, the length of the diagonal \( x \) on the bottom face of the cube is approximately **19.8**.