The area of rectangular hallway is 120 square feet. If the length and the width are both composite numbers, what are the possible dimensions of the hallway?
10 by 12
8 by 15
6 by 20
5 by 24
4 by 30
3 by 40
i don't knw
To find the possible dimensions of the hallway, we need to list all the composite number pairs whose product is equal to 120. We can do this by finding the factors of 120.
The factors of 120 are:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Now, let's find the pairs of composite numbers whose product is 120:
2 × 2 = 4 (4 is composite)
2 × 3 = 6 (2 and 3 are both composite)
2 × 4 = 8 (8 is composite)
2 × 5 = 10 (2 and 5 are both composite)
2 × 6 = 12 (2 and 6 are both composite)
...
Continuing this process, we can find all the possible pairs of composite numbers. The possible dimensions of the rectangular hallway are:
4 feet × 30 feet
6 feet × 20 feet
8 feet × 15 feet
10 feet × 12 feet
So, the possible dimensions of the rectangular hallway are 4 feet by 30 feet, 6 feet by 20 feet, 8 feet by 15 feet, and 10 feet by 12 feet.