Question

I am also going to wallpaper the living room. The living room has 2 doors, each the same size as the bedroom door. The height and width are the same in the living room as in the bedroom. The length of the living room is 3 times the width of the living room. Write an expression detailing how much wallpaper is needed for the living room (rectangular).

a) 12W^2 square feet
b) 8W^2 square feet
c) 9W^2 square feet
d) 6W^2 square feet

Answer 1

The expression detailing how much wallpaper is needed for the living room in terms of the width squared would be 8W^2, assuming the height equals the width and we're not accounting for windows or doors. However, there seems to be an error in the question as we cannot arrive at a final expression solely in terms of W² with the given information.

Step-by-step explanation:

To calculate the wallpaper needed for the living room, we need to know the dimensions of the living room and the size of the doors that will not be wallpapered. We're given that the length of the living room is three times its width. We can represent the width as W and the length as 3W. The living room's height is the same as the bedroom, but since that is not specified, it doesn't matter for calculating area in terms of W.

The total area of the walls is the perimeter of the room times the height, which we can denote as H. Since we have a rectangular room, the perimeter is 2*(W + 3W), giving us 8W. Multiplying this by the height gives us an area of 8WH. We also must subtract the areas of the two doors. Since each door is the same size as the bedroom door, let's denote each door's area as D. The total area to subtract for the doors is 2D. However, these details are not necessary as the door sizes and room height do not affect the expression in terms of W, since we are asked to ignore the doors.

Therefore, the expression we're looking for only in terms of W will be the perimeter times the height, minus the doors. Since we ignore the doors and the height, the expression only regarding width would be Perimeter x Height in terms of W, which is 8W x height. However, without knowing the height or needing to consider the doors, we cannot arrive at a final expression in terms of W². It appears there might be a mistake in the question as it stands, or there is not enough information given to answer it correctly.

If we only consider the given options as possible answers and assume a height (H) that is also equal to W for simplicity, then the area of wallpaper needed would simply be 8W² assuming height equals width and we're not accounting for windows or doors, which aligns with option (b).