Question

Write the expression for the amount of wallpaper in square feet you need to cover the living room, which is the same height and width as the family room, but it has a length that is 5 times greater than the height. The living room has 2 doors.

Answer 1

The expression for the amount of wallpaper needed is
`20b^(2)- 2d`

Explanation:

The necessary dimensions of the living room we need are the length and the height. We will not be needing the width because we will not be covering the floors with any wallpaper.

We will now assign variables to represent the surface areas of some features of the rooms.

Let the length of one wall of the living room be = l cm

Let the breadth of one wall of the living room be = b cm

Let the surface area of the doors be = d
`cm^(2)`

From the problem, we know that l = 5b

The area to be covered on one wall of the living room will be = length X breadth.

l X b

recall l = 5b

`5b * b = 5b^(2)`

this is the area to be covered on one wall.

For the four walls, we would have
`4 * 5b^(2)= 20b^(2)`

Let us remember that the living room has two doors each covering a surface area of
`d cm^(2)` we will have to subtract these out since hey won't be covered.

`20b^(2)- 2d`

Therefore, the expression for the amount of wallpaper needed is
`20b^(2)- 2d`