One side of the rectangle was reduced by 20%, and then both sides were enlarged by 20%.

One side of the rectangle was reduced by 20%, and then both sides were enlarged by 20%. It turned out that the perimeter did not change. How many times is the rectangle longer than its width?

Suppose the sides of the rectangle were equal to x and y.

When x was reduced by 20%, it turned out:

x * (100 – 20): 100 = 0.8 * x.

Then both sides increased by 20%.

One side turned out:

y * (100 + 20): 100 = 1.2 * y.

the second side turned out:

0.8 * x * (100 + 20): 100 = 0.8 * x * 1.02 = 0.96 * x.

Originally, the perimeter of the rectangle was:

2 * (x + y).

After changing the sides, the perimeter became equal to:

2 * (0.96 * x + 1.2 * y).

We get:

2 * (x + y) = 2 * (0.96 * x + 1.2 * y),

x + y = 0.96 * x + 1.2 * y,

0.04 * x = 0.2 * y,

x = 5 * y.

Answer: 5 times.