Multiple choice general knowledge math & puzzles

A rectangle is such that it can be perfectly cut into smaller squares of a maximum possible side of length 12 units. It is also known that the perimeter of such a rectangle is 384 units. How many distinct rectangles satisfy the criteria given..

  1. 4

  2. 3

  3. 8

  4. 6

  5. 10

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let sides be 12x and 12y where x,y are coprime. Perimeter 2(12x + 12y) = 384, so x + y = 16. Coprime pairs (x,y) for 16 are (1,15), (3,13), (5,11), (7,9). There are 4 distinct pairs, representing 4 distinct rectangles.