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

Let x be the length of one of the sides of the rectangle. Since one side of the rectangle is 11 times smaller than the other, the value of the second side of the rectangle is x / 11 cm.The sum of the two sides of the rectangle is equal to the value of half of the perimeter, so we can write the equation: x + x / 11 = 312/2, x + x / 11 = 156. To solve the equation, multiply the right and left sides of the equation by the number 11: 11 (x + x / 11) = 11 * 156, 11x + x = 1716, 12x = 1716, x = 143. One side of the rectangle is 143 cm, and the second side is equal to 143/11 = 13 cm.The area of the rectangle is: S = 13 cm * 143 cm = 1859 cm square.