Sam is going to tile a rectangular room that has an area of 64 square feet. He will be using square tiles that measure 1/4 square feet.
If the dimensions of the sun room are to be whole numbers in feet, list all of the possible sets of dimensions (length & width) FOR THE SUN ROOM AS WELL as the total number of tiles needed for each pair of dimensions that you give.
Where do I start?
For an area of 64 square feet, the dimensions being whole numbers, the possible cases are :
l w
----
1,64 ----rather silly
2,32 --- still silly
4,16
8,8
16,4
32,2 ---- getting silly again
64,1
each gives an area of 64 square feet, each will need 64 รท 1/4 or 256 tiles
To find all the possible sets of dimensions for the sunroom, you can start by determining the factors of the area given.
First, calculate the area of the sunroom, which is 64 square feet.
Factors of 64: 1, 2, 4, 8, 16, 32, 64
These factors represent possible dimensions for the sunroom. However, we need to ensure that the dimensions are whole numbers.
Next, we will check which of these factors can form whole number dimensions.
Possible sets of dimensions for the sunroom:
1. Length = 1 ft, Width = 64 ft (1 tile)
2. Length = 2 ft, Width = 32 ft (2 tiles)
3. Length = 4 ft, Width = 16 ft (16 tiles)
4. Length = 8 ft, Width = 8 ft (64 tiles)
5. Length = 16 ft, Width = 4 ft (16 tiles)
6. Length = 32 ft, Width = 2 ft (2 tiles)
7. Length = 64 ft, Width = 1 ft (1 tile)
For each set of dimensions, the total number of tiles needed can be calculated by dividing the area of the sunroom by the area of each tile.
Total number of tiles needed for each set of dimensions:
1. 64 sq ft / (1/4 sq ft) = 256 tiles
2. 64 sq ft / (1/4 sq ft) = 128 tiles
3. 64 sq ft / (1/4 sq ft) = 64 tiles
4. 64 sq ft / (1/4 sq ft) = 64 tiles
5. 64 sq ft / (1/4 sq ft) = 64 tiles
6. 64 sq ft / (1/4 sq ft) = 128 tiles
7. 64 sq ft / (1/4 sq ft) = 256 tiles
Now, you have the possible sets of dimensions for the sunroom as well as the total number of tiles needed for each set.