Find the perimeter of a rectangle if its area is 175 and the ratio of adjacent sides is 1: 7.

We write down the length of one of the sides of the rectangle equal to x cm.

Since we know that the lengths of the sides are 1: 7, then the length of the second side will be: 7 * x.

Since the area is the product of two sides, we get:

x * 7 * x = 175.

7 * x ^ 2 = 175.

x ^ 2 = 175/7 = 25.

x = √25 = 5 cm (first side).

So the second will be equal to:

7 * x = 7 * 5 = 35 cm.

To find the perimeter of a shape, multiply the sum of the two sides by 2 equal parts.

As a result, it will be:

2 * (5 + 35) = 2 * 40 = 80 cm.

Answer: 80 cm.