One side of the rectangle was reduced by 20% and the other was increased by x%.

One side of the rectangle was reduced by 20% and the other was increased by x%. It turned out that the perimeter and area did not change. Find x.

Let a be the first side of the rectangle and b the second. Then 0.8a is side a after changing its length. Let y be the decimal by which you need to multiply the side of the rectangle b so that it increases by x%.
P – perimeter, S – area.
P1 = 2a + 2b, S1 = ab.
P2 = 1.6a + 2yb, S2 = 0.8a * yb.
By condition, Р1 = Р2, S1 = S2, that is:
2a + 2b = 1.6a + 2yb.
ab = 0.8y * ab, whence it follows:
1 = 0.8y
y = 1 / 0.8 = 1.25.
That is, b has increased by 25%.