Ms. Fisher is using 64 carpet tiles to make a reading area in her classroom. Each tile is square that measures 1 foot by 1 foot. What is.the length and width of the rectangular area she can make with the smallest possible perimeter?
Thanks we thought 8x8 but not sure
You're welcome.
Which would have the smaller perimeter?
4 by 16 or 8 by 8?
Ms fisher ls using 64 carpet squares to make a reading area in her classroom.Each square measures 1 foot by 1 foot.she wants to arrange the 64 squares in a rectangular shape with the smallest possible perimeter.what
dimensions should she use for her reading area?
Well, isn't Ms. Fisher creative! Now, let's calculate this. We have 64 carpet tiles, and each tile measures 1 foot by 1 foot. We want to find the length and width of the rectangular area with the smallest possible perimeter.
To do this, we need to find the factor pairs of 64. The factor pairs are pairs of numbers that, when multiplied together, give us 64. For example, 1 and 64, 2 and 32, and so on.
Let's find the factor pairs of 64: 1 * 64, 2 * 32, 4 * 16, 8 * 8.
Now, let's calculate the perimeters of each of these pairs:
- 1 * 64 gives us a perimeter of 130 feet (1 + 64 + 1 + 64 = 130).
- 2 * 32 gives us a perimeter of 68 feet (2 + 32 + 2 + 32 = 68).
- 4 * 16 gives us a perimeter of 40 feet (4 + 16 + 4 + 16 = 40).
- 8 * 8 gives us a perimeter of 32 feet (8 + 8 + 8 + 8 = 32).
So, the rectangular area with the smallest possible perimeter would be 8 feet by 8 feet.
To find the length and width of the rectangular area with the smallest possible perimeter, we need to determine the dimensions that result in the smallest perimeter.
Given that each carpet tile is 1 foot by 1 foot, we can calculate the total area of the carpet tiles as follows:
Total Area = Number of Tiles × Area of Each Tile
In this case, the number of tiles Ms. Fisher has is 64, and the area of each tile is 1 foot by 1 foot. Therefore:
Total Area = 64 × (1 ft × 1 ft) = 64 square feet
Now, let's consider the dimensions of the rectangular area. Suppose the length is L and the width is W.
The perimeter of a rectangle is given by the equation:
Perimeter = 2 × (Length + Width)
Since we want to find the dimensions with the smallest perimeter, we can rewrite the equation as:
Perimeter = 2L + 2W
Now, we need to find the values of L and W that minimize the perimeter while still maintaining an area of 64 square feet.
One way to approach this problem is to use the concept of finding the dimensions of a rectangle with a given area that has the smallest possible perimeter. In this case, the given area is 64 square feet.
To solve for the dimensions, we can start by finding the square root of 64:
√64 = 8
So, the dimensions of the rectangle with an area of 64 square feet are 8 feet by 8 feet.
Substituting these values into the perimeter equation, we get:
Perimeter = 2 × 8 ft + 2 × 8 ft = 32 feet
Therefore, the length and width of the rectangular area she can make with the smallest possible perimeter is 8 feet by 8 feet.