the floor of a room is rectangle in shape its length is 5 meter and breadth is 4 mete. the area of its four walls is 108 sq.m. find its height
First thing I do is draw a picture.
Sur Area of the four walls = 2 x (height of wall x width) + 2 x (height of wall x length), which yields:
108 = 2 x (h x 5) + 2 x (h x 4).
So height = 6 meters
hw+hl = 54
5h+4h = 54
h = 9
To find the height of the room, we can use the formula for the perimeter of a rectangle and the formula for the area of a rectangle.
Let's start by calculating the perimeter of the room. The perimeter is equal to two times the sum of the length and breadth of the rectangle.
Perimeter = 2 × (Length + Breadth)
Perimeter = 2 × (5m + 4m)
Perimeter = 2 × (9m)
Perimeter = 18m
Now, we need to find the height of the room. The area of the four walls (excluding the floor and ceiling) is given as 108 square meters.
Since the room is a rectangular prism, the area of the four walls is equal to the perimeter multiplied by the height of the room.
Area of Four Walls = Perimeter × Height
108 sq.m = 18m × Height
To solve for the height, we divide both sides of the equation by the perimeter:
Height = 108 sq.m / 18m
Height = 6m
Therefore, the height of the room is 6 meters.