Find the area of a rectangle if its perimeter is 144 and the ratio of neighboring sides is 1: 7.

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

According to the condition of the problem, the ratio of the lengths of the adjacent sides of this rectangle is 1: 7, therefore, the length of the larger side of this rectangle will be 7x.

It is also known that the perimeter of this rectangle is 144, therefore, we can make the following equation:

2 * (x + 7x) = 144.

We solve the resulting equation:

2 * 8x = 144;

16x = 144;

x = 144/16;

x = 9.

Therefore, the length of the longer side of this rectangle is 7x = 7 * 9 = 63, and the area of ​​this rectangle is 63 * 9 = 567.

Answer: the area of ​​this rectangle is 567.