Amystery number is greater than 50 and less than 100. you can make exactly five different rectangles with the mystery number of tiles. (hint: this means the mystery number is a square number). its prime factorization consists of only one prime number. what is the mystery number?

81

Step-by-step explanation:

We know the number is between 50 and 100.  The prime factorization consists of only one prime number, so the number must be a perfect square.  The possible numbers are 64 and 81.

The rectangles that can be made with 64 tiles are:

1×64, 2×32, 4×16, 8×8, 16×4, 32×2, 64×1

The rectangles that can be made with 81 tiles are:

1×81, 3×27, 9×9, 27×3, 81×1

There are 7 rectangles that can be made with 64 tiles.  There are only 5 rectangles that can be made with 81 tiles.  Therefore, the mystery number is 81.