The lengths of the sides of the rectangle are reciprocal numbers. The sum of the digits of one of them

The lengths of the sides of the rectangle are reciprocal numbers. The sum of the digits of one of them is 11. Find the perimeter of the rectangle.

Mutually reciprocal numbers are two numbers that, when multiplied, give the result 1. According to the condition of the problem, the sum of digits is set to 11. These numbers can include the numbers 29, 38, 47, 56, 65, 74, 83, 92.

The perimeter of a rectangle is the sum of all sides. In order to find the perimeter of a rectangle, you need to:

P = 2a + 2b, P is the perimeter of the rectangle, a is the length of the rectangle, b is the width of the rectangle.

Let’s find all possible perimeters:

P = 2 * 29 + 2 * 1/29 = 58 + 2/29 = 58 2/29;

P = 2 * 38 + 2 * 1/38 = 76 + 1/19 = 78 1/19;

P = 2 * 47 + 2 * 1/47 = 94 + 2/47 = 94 2/47;

P = 2 * 56 + 2 * 1/56 = 112 + 1/28 = 112 1/28;

P = 2 * 65 + 2 * 1/65 = 130 + 2/65 = 130 2/65;

P = 2 * 74 + 2 * 1/74 = 148 + 1/37 = 148 1/37;

P = 2 * 83 + 2 * 1/83 = 166 + 2/83 = 166 2/83.