a rectangular garage has a floor area of 240 square feet. What are all the possible length and width
There are an infinite number of possibilities, since length L and Width W do not have to be integers.
For any length L, W = 240/L.
To find all the possible length and width combinations that satisfy a rectangular garage with a floor area of 240 square feet, we can start by listing all the factors of 240. Factors are numbers that can divide 240 without leaving a remainder.
The factors of 240 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.
Now, let's pair up these factors to get all the possible length and width combinations:
Length: 1, Width: 240 (1 x 240)
Length: 2, Width: 120 (2 x 120)
Length: 3, Width: 80 (3 x 80)
Length: 4, Width: 60 (4 x 60)
Length: 5, Width: 48 (5 x 48)
Length: 6, Width: 40 (6 x 40)
Length: 8, Width: 30 (8 x 30)
Length: 10, Width: 24 (10 x 24)
Length: 12, Width: 20 (12 x 20)
Length: 15, Width: 16 (15 x 16)
Length: 16, Width: 15 (16 x 15)
Length: 20, Width: 12 (20 x 12)
Length: 24, Width: 10 (24 x 10)
Length: 30, Width: 8 (30 x 8)
Length: 40, Width: 6 (40 x 6)
Length: 48, Width: 5 (48 x 5)
Length: 60, Width: 4 (60 x 4)
Length: 80, Width: 3 (80 x 3)
Length: 120, Width: 2 (120 x 2)
Length: 240, Width: 1 (240 x 1)
These are all the possible combinations of length and width for a rectangular garage with a floor area of 240 square feet.