The sides of the rectangle are 3: 4, and its diagonal is 50 cm. Find the perimeter of the rectangle.

Let’s take the side as 3 * x, then the second will be equal to 4 * x.
By the Pythagorean theorem we get:
(3 * x) ^ 2 + (4 * x) ^ 2 = 50 ^ 2
9 * x ^ 2 + 16 * x ^ 2 = 2500
25 * x ^ 2 = 2500
x ^ 2 = 100
x = 10
Then one side is equal to:
3 * 10 = 30, and the second:
4 * 10 = 40
The perimeter will be equal to:
2 * (30 + 40) = 2 * 70 = 140.