Explanation:

- We know the area and perimeter of the rectangle: Area = 480 cm², Perimeter = 92 cm.

- Let the length be $l$ and width be $w$.

- With $l\times w=480$ and $2(l+w)=92$, solve for $l$ and $w$.

- From the perimeter, $l+w=46$.

- Solve the system of equations:

1. $l\times w=480$

2. $l+w=46$

- Using these equations, find $l$ and $w$.

- Use the Pythagorean theorem: Diagonal $d=\sqrt{l^2+w^2}$.

- Solve for the diagonal using the expressions from the system of equations.

After solving, the size of the LCD based on its diagonal is 39 cm.

Therefore, Option 2, 39 cm, is correct. .