The perimeter of the rectangle is 312cm. Find its area if one side of the rectangle is 11 times smaller than the other.

1. Let the smaller side of the rectangle be equal to y, then the large side is equal to 11y. By adding these sides and doubling their sum, we get the perimeter. Let’s solve the composed equation:

(y + 11y) * 2 = 312

12y * 2 = 312,

24y = 312,

y = 312/24,

y = 13.

2. Find the large side of the rectangle:

11 * 13 = 143.

3. Find the area of the rectangle by the formula S = a * b, where S is the area of the rectangle, and and b are the adjacent sides of the rectangle:

S = 143 * 13 = 1859 cm2.

Answer: the area of the rectangle is 1859 cm2.