A rectangular room is 10 feet longer than it is wide. One-foot-by-one-foot tiles cover the entire floor. Let w represent the width (in feet) of the room. Write an expression in simplest form that represents the number of tiles along the outside of the room.
Simplified Expression=
p = 2(w + w+10)
To find the expression that represents the number of tiles along the outside of the room, we first need to find the perimeter of the room.
The perimeter of a rectangle can be found by adding the lengths of all four sides. In this case, the length of the room is 10 feet longer than the width.
Let's say the width of the room is represented by w. Then, the length of the room can be represented as w + 10.
The perimeter of the room is then given by the formula:
Perimeter = 2(length + width)
Substituting the values, we have:
Perimeter = 2(w + 10 + w)
= 2(2w + 10)
= 4w + 20
Now, since each tile is 1 foot by 1 foot, to find the number of tiles along the outside of the room, we divide the perimeter by the length of one side of a tile (which is 1 foot):
Number of tiles along the outside = Perimeter / 1
= 4w + 20
Therefore, the simplified expression that represents the number of tiles along the outside of the room is 4w + 20.
To find the number of tiles along the outside of the room, we need to calculate the perimeter of the room.
The perimeter of a rectangle can be calculated by adding up all four sides.
Given that the width of the room is represented by "w," and the length is 10 feet longer than the width, the length can be represented as "w + 10."
Therefore, the perimeter of the room can be calculated as follows:
Perimeter = 2(width) + 2(length)
Perimeter = 2w + 2(w + 10)
Simplifying this expression gives:
Perimeter = 2w + 2w + 20
Perimeter = 4w + 20
So, the simplified expression for the number of tiles along the outside of the room is 4w + 20.