Find the perimeter of a rectangle if its area is 272 and the ratio of adjacent sides is 4:17.

We know the ratio of the sides of the rectangle, a: b = 4: 17, if we introduce the proportionality coefficient k, then we can say that a = 4k, b = 17k.

By the known area of the rectangle and the formula for finding it: S = a • b, we get the following equation:

4k • 17k = 272;

68 • k ^ 2 = 272;

k ^ 2 = 272: 68;

k ^ 2 = 4.

Where, k = 2 or k = -2.

But there can be no negative roots in the length problem, so k = 2.

Reverse replacement and: a = 4 • 2 = 8; b = 17 • 2 = 34.

Perimeter of the rectangle: P = 2 • (a + b).

We get:

P = 2 • (8 + 34) = 84.

Answer: 84.