Final answer:
By using the given floor area and the relationship between the room's dimensions, we can solve for the breadth and subsequently the length of the room. We then apply these to the formula for the area of the walls to find the room's height, which is 4 meters.
Step-by-step explanation:
The student is seeking to find out the height of a room given the area of the walls and the floor, as well as the relationship between the room's length and breadth. This is a problem related to geometry and algebra.
We start with the total area of the four walls, which is 600 sq. meters. The total area of the four walls can be calculated by the formula: 2(height x length) + 2(height x breadth). Since the floor area is 1250 sq. meters and the room is rectangular, we can deduce that the length (l) is twice the breadth (b). So, the floor area (which is the same as the ceiling area) is given by the product length x breadth, or 2b x b = 1250 sq. meters, leading to b^2 = 625 and b = 25 meters. The length is twice the breadth, so l = 50 meters.
Now, we apply the given dimensions to the formula for the area of the walls: 2(height x 50) + 2(height x 25) = 600. This simplifies to 100(height) + 50(height) = 600, or 150(height) = 600. Divide both sides by 150 to find the height: height = 600 / 150, which yields a height of 4 meters.