The area of a rectangular hallway is 120 square feet. If the length and the width are both composite numbers what are the possible dimensions of the hallway? Would it be 40 by 4?
so you want LW = 120
where L and W are composite , where composite means not prime
120 = (using integers only)
1 x 120
2x60
3x40 *
4x30 *
5x24
6x20 *
8x15 *
10x12 *
I have labeled the ones without a prime number with an *
so I count 5 of them
Your choice of 40 by 4 wouldn't even give us our correct area of 120
To find the possible dimensions of the hallway, we need to factorize the area of 120 square feet into composite numbers.
Factorizing 120:
The prime factorization of 120 is 2^3 * 3 * 5.
Now, let's consider the dimensions of the hallway:
If we set one dimension as 2^3 (which is 8), then the other dimension should be the remaining factors, which are 3 * 5 = 15. Thus, one possible dimension is 8 by 15.
Alternatively, if we set one dimension as 2^2 (which is 4), then the other dimension should be the remaining factors, which are 2 * 3 * 5 = 30. Thus, another possible dimension is 4 by 30.
So, the possible dimensions for a rectangular hallway with an area of 120 square feet, where both length and width are composite numbers, are 8 by 15 and 4 by 30.