The rectangle has a perimeter of 38 cm and is one whole five-seventh times its width. Find the area of the rectangle.

1. Let the smaller side of the rectangle x cm. Then, according to the problem statement, the larger side is equal to:

y = 1 5/7 * x = 12/7 * x.

2. Let’s make an equation for the perimeter of our rectangle:

2 (x + y) = 38;
x + y = 38: 2;
x + y = 19;
x + 12/7 * x = 19;
x (1 + 12/7) = 19;
19/7 * x = 19;
1/7 * x = 1;
x = 7 (cm);
y = 19 – x = 19 – 7 = 12 (cm).
3. The area of the rectangle is equal to the product of the sides:

S = xy = 7 * 12 = 84 (cm ^ 2).

Answer. Rectangle area: 84 cm ^ 2.