The sides of the rectangle are 3: 4. Find the percentage of the rectangle’s perimeter to the smaller side.

Let’s denote by x the length of the shorter side of this rectangle.

According to the condition of the problem, the lengths of the sides of this rectangle are related as 3: 4, therefore, the length of the larger side of this rectangle is (4/3) x.

Find the perimeter P of this rectangle:

P = 2 * (x + (4/3) x) = 2 * ((3/3) x + (4/3) x) = 2 * (7/3) x = (14/3) x.

Find the percentage of the rectangle’s perimeter to the length of the smaller side of the rectangle:

100 * (14/3) x / x = 100 * (14/3) = 1400/3 = 466 2/3%.

Answer: The ratio of the perimeter of the rectangle to the length of the smaller side is 466 2/3%.