Find the perimeter of a rectangle if its area is 250 and the ratio of the lengths of adjacent sides is 5: 8.

Let’s find the lengths of the sides of this rectangle.

Let’s denote by x one fifth of the smaller side of this rectangle.

Then the length of this side will be 5x.

According to the condition of the problem, the lengths of the adjacent sides of this rectangle are related as 5: 8, therefore, the length of the larger side of this rectangle will be 8x.

It is also known that the area of ​​this rectangle is 250, therefore, we can draw up the following equation:

8x * 5x = 250.

Solving this equation, we get:

40x ^ 2 = 250;

x ^ 2 = 250/40;

x ^ 2 = 25/4;

x ^ 2 = (5/2) ^ 2;

x = 5/2.

Knowing x, we find the perimeter of this rectangle:

2 * (5x + 8x) = 2 * 13x = 26x = 26 * (5/2) = 13 * 5 = 65.

Answer: The perimeter of this rectangle is 65.