Mike has made a rectangle using 48 square tiles. If he adds the length and width of his rectangle together he gets a prime number. What is the length and width of the rectangle?
If he adds length and width to get a prime, then their sum must be odd. So, one of the terms is even, the other odd. The only factors of 48 that fit these conditions are 3 and 16
3*16 = 38
3+16 = 19 a prime
oops: 3*16 = 48
To find the length and width of the rectangle, we need to consider the prime numbers and find the pair that satisfies the given conditions.
First, let's list down some prime numbers and their sum:
2 + 2 = 4 (not prime)
2 + 3 = 5 (prime)
2 + 5 = 7 (prime)
2 + 7 = 9 (not prime)
3 + 3 = 6 (not prime)
3 + 5 = 8 (not prime)
3 + 7 = 10 (not prime)
5 + 5 = 10 (not prime)
5 + 7 = 12 (not prime)
7 + 7 = 14 (not prime)
From the above calculations, we can see that the only pair of prime numbers where their sum is a prime number is 2 and 3.
Now let's apply this to the given information:
Since Mike has used 48 square tiles, we can consider the sides of the rectangle as factors of 48.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
We need to find a pair of factors whose sum is a prime number.
Checking the pairs:
1 + 48 = 49 (not prime)
2 + 24 = 26 (not prime)
3 + 16 = 19 (prime)
4 + 12 = 16 (not prime)
6 + 8 = 14 (not prime)
Therefore, the length of the rectangle is 3 tiles and the width is 16 tiles.