1. **State the problem:** Calculate the total surface area of a rectangular box with length $90$ cm, width $60$ cm, and height $50$ cm. 2. **Formula:** The total surface area $A$ of a rectangular box is given by: $$A = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Substitute the values:** $$A = 2(90 \times 60 + 90 \times 50 + 60 \times 50)$$ 4. **Calculate each product:** $$90 \times 60 = 5400$$ $$90 \times 50 = 4500$$ $$60 \times 50 = 3000$$ 5. **Sum the products:** $$5400 + 4500 + 3000 = 12900$$ 6. **Multiply by 2:** $$A = 2 \times 12900 = 25800$$ 7. **Answer:** The total surface area of the box is $25800$ cm². This matches the option $25800$ cm².