Answer: 7, 7, 19, and 19
Recall that a rectangle has congruent parallel sides, meaning the sides opposite are equivalent in length. Therefore, 2 sides are both 12 cm longer than the other two sides. Let's write an equation:
Let x be the shorter side, and x + 12 be the longer side.
x + x + (x + 12) + (x + 12) = 52
Combine like terms.
4x + 24 = 52
4x = 28
x = 7
Therefore, the shorter sides are 7, and the longer sides are 19