The length of a rectangular rug is twice its width. The rug is centered in a rectangular room. Each edge is 3ft. From the nearest wall. What is the area of the room?
the rug is w x 2w
The room is thus (w+6) x (2w+6)
Not knowing either the width or the area of the rug, it's hard to put a number on the area of the room.
To find the area of the room, we need to determine the dimensions of the rug and then calculate the total area.
Let's start by defining the width of the rug. We're given that the length of the rug is twice its width. Let's represent the width as "w". Therefore, the length will be "2w".
Given that the rug is centered in the room, we can determine the length and width of the room using the dimensions of the rug.
When the rug is centered, the distance from its edge to the nearest wall is 3ft. So, the length of the room is equal to the length of the rug plus twice this distance: 2w + 2(3ft).
Similarly, the width of the room is equal to the width of the rug plus twice this distance: w + 2(3ft).
Now, we know the dimensions of the room, so we can calculate its area by multiplying the length and width:
Area of the room = (length of the room) * (width of the room)
= (2w + 2(3ft)) * (w + 2(3ft))
= (2w + 6ft) * (w + 6ft)
= 2w^2 + 12w + 6w + 36ft^2
= 2w^2 + 18w + 36ft^2.
Therefore, the area of the room is given by the expression 2w^2 + 18w + 36ft^2.