Older television screens have an aspect ratio of $ 4: 3$. That is, the ratio of the width to the height is $ 4: 3$. The aspect ratio of many movies is not $ 4: 3$, so they are sometimes shown on a television screen by 'letterboxing' - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of $ 2: 1$ and is shown on an older television screen with a $ 27$-inch diagonal. What is the height, in inches, of each darkened strip?
[asy]unitsize(1mm);
defaultpen(linewidth(.8pt));
filldraw((0,0)--(21.6,0)--(21.6,2.7)--(0,2.7)--cycle,grey,black);
filldraw((0,13.5)--(21.6,13.5)--(21.6,16.2)--(0,16.2)--cycle,grey,black);
draw((0,2.7)--(0,13.5));
draw((21.6,2.7)--(21.6,13.5));[/asy]$ \textbf{(A)}\ 2 \qquad \textbf{(B)}\ 2.25 \qquad \textbf{(C)}\ 2.5 \qquad \textbf{(D)}\ 2.7 \qquad \textbf{(E)}\ 3$
1. **Determine the dimensions of the television screen:**
   The aspect ratio of the television screen is \(4:3\). Let the width be \(4x\) and the height be \(3x\). The diagonal of the screen is given as 27 inches. Using the Pythagorean theorem, we can write:
   \[
   (4x)^2 + (3x)^2 = 27^2
   \]
   Simplifying, we get:
   \[
   16x^2 + 9x^2 = 729
   \]
   \[
   25x^2 = 729
   \]
   \[
   x^2 = \frac{729}{25}
   \]
   \[
   x = \sqrt{\frac{729}{25}} = \frac{27}{5} = 5.4
   \]

2. **Calculate the width and height of the television screen:**
   Using \(x = 5.4\):
   \[
   \text{Width} = 4x = 4 \times 5.4 = 21.6 \text{ inches}
   \]
   \[
   \text{Height} = 3x = 3 \times 5.4 = 16.2 \text{ inches}
   \]

3. **Determine the dimensions of the movie screen:**
   The aspect ratio of the movie is \(2:1\). Let the width of the movie be \(2y\) and the height be \(y\). Since the movie is shown on the television screen, the width of the movie must match the width of the television screen:
   \[
   2y = 21.6
   \]
   \[
   y = \frac{21.6}{2} = 10.8 \text{ inches}
   \]

4. **Calculate the height of the darkened strips:**
   The height of the movie on the screen is 10.8 inches, while the height of the television screen is 16.2 inches. The difference in height is:
   \[
   16.2 - 10.8 = 5.4 \text{ inches}
   \]
   Since there are two darkened strips (one at the top and one at the bottom), the height of each strip is:
   \[
   \frac{5.4}{2} = 2.7 \text{ inches}
   \]

The final answer is \(\boxed{2.7}\).