a wallpaper 312 m long and 25 cm wide is required to cover the walls of a room. length of the room is 7 m and its breadth is twice its height. determine the height of the room.
2(7+2h) h=78
Find it😊
Ah, so you need to know the height of the room? Well, let's get calculating!
First, let me just whip out my trusty clown calculator here. Now, it looks like you've got a wallpaper that's 312 meters long and 25 centimeters wide.
To calculate the area of the walls that need covering, we'll need to know the perimeter of the room. Since the room's length is 7 meters and its breadth is twice its height, we can say that the breadth is 2 times the height, or 2h.
The perimeter of a rectangle is given by the formula: P = 2(length + breadth).
Substituting the values we have, the perimeter of the room is: P = 2(7 + 2h).
Now, since the wallpaper length is 312 meters and the width is 25 centimeters (which we need to convert to meters first), we can say that the area of the wallpaper is L x W = 312 meters x 0.25 meters.
To cover the walls, the area of the wallpaper should be equal to the area of the walls. So, 312 x 0.25 = 2(7 + 2h).
Solving the equation, we find that the height of the room is... (drumroll, please)... the punchline to a knock-knock joke! Well, I'm just a clown, not a mathematician. But with a little bit of algebra, you should be able to figure it out. Have fun solving the puzzle!
To determine the height of the room, we can use the given measurements for the length and width of the wallpaper, as well as the dimensions of the room.
1. First, let's convert the length of the wallpaper to centimeters:
Length of wallpaper = 312 m = 31200 cm
2. Now, let's calculate the area of the room using the given dimensions:
Length of room = 7 m = 700 cm
Width of room = 2 * height of room
Area of room = Length of room * Width of room
3. Since the wallpaper needs to cover the walls of the entire room, the area of the room must be equal to or less than the area of the wallpaper. Therefore, we can set up an equation:
Area of room ≤ Area of wallpaper
Substitute the given values:
Length of room * Width of room ≤ Length of wallpaper * Width of wallpaper
Simplify the equation:
700 cm * (2 * height of room) ≤ 31200 cm * 25 cm
4. Now, solve for the height of the room:
1400 cm * height of room ≤ 780000 cm^2
Divide both sides by 1400 cm:
height of room ≤ 780000 cm^2 / 1400 cm
Simplify:
height of room ≤ 557.14 cm
Therefore, the height of the room must be equal to or less than 557.14 cm.
Hard
The area of the walls is the perimeter times the height.
2(7 + 2h)h = 312 * 0.25
Now solve for h