The area of the four walls of a room is $120 \text{ m}^2$ and the length is twice the breadth. If the height of the room is $4\text{ m}$, then the area of the floor is

### Concept & Surface Area of Walls The area of four walls of a room is given by the lateral surface area formula. $$ \text{Area of 4 walls} = 2(l + b)h $$ ### Step-by-Step Solution * Given height $h = 4 \text{ m}$ and the area of the four walls = $120 \text{ m}^2$. * Let the breadth of the room be $b$. According to the problem, the length is $l = 2b$. * Substitute the known values into the area formula: $2(2b + b) \times 4 = 120$. * Simplify the equation: $2(3b) \times 4 = 120 \Rightarrow 24b = 120$. * Solving for breadth gives $b = 5 \text{ m}$. * Since length is twice the breadth, $l = 2 \times 5 = 10 \text{ m}$. * The area of the floor is given by $l \times b$. Thus, Floor Area = $10 \times 5 = 50 \text{ m}^2$. ### Exam Strategy & Shortcut Notice that the floor area is $l \times b = (2b) \times b = 2b^2$. By simplifying the wall area formula to $24b = 120$, we immediately find $b=5$. We just need $2(5^2) = 50$, avoiding the need to write down every individual dimension. ### Common Pitfall A frequent error is confusing the total surface area of a cuboid with the area of its four walls. Remember that the four walls formula explicitly excludes the floor and ceiling. ### Final Answer Therefore, the correct answer is **$50 \text{ m}^2$**.