One side of the rectangle is a m, and the other is 9 times larger. The smaller side was enlarged by 2 times

One side of the rectangle is a m, and the other is 9 times larger. The smaller side was enlarged by 2 times, and the larger one was reduced by 3 times. Has the perimeter of the rectangle increased or decreased, and how many times?

The first rectangle has dimensions:
width is equal to a;
the length is (9 * a).
Let’s find what the perimeter of this rectangle is:
P1 = 2 * (a + 9 * a) = 20 * a.

The second rectangle has dimensions:
width – (2 * a);
length – (9 * a) / 3 = 3 * a.
Let’s calculate what the perimeter of the second rectangle is:
P2 = 2 * (2 * a + 3 * a) = 2 * 5 * a = 10 * a.

Determine how many times the first perimeter is greater than the second:
P1 / P2 = 20 * a / (10 * a) = 2.

Answer: the perimeter of the rectangle will decrease by 2 times.