The length of the rectangle is 14 cm. The length of the side of the square is 11 m.

The length of the rectangle is 14 cm. The length of the side of the square is 11 m. What is the area of the rectangle if the perimeter of the rectangle and the square are equal?

The width of this rectangle is denoted by x (in centimeters). Then the perimeter of the rectangle P will be equal to P = 2 * (14 + x) cm.
Since, according to the terms of the assignment, the length of the side of the square is 11 meters, then taking into account that 1 m = 100 cm, we get: the length of the side of the square is 11 * 100 cm = 1100 cm.Then the perimeter of the square is 4 * 1100 cm = 4400 cm.
By the condition of the task, the perimeter of the rectangle and the square are equal. Therefore, 2 * (14 + x) = 4400 or 14 + x = 2200, whence x = 2200 – 14 = 2186. Therefore, the required area S is equal to (14 cm) * (2186 cm) = 30604 cm².
It should be noted that, in all likelihood, the authors of the assignment made a typo when filling out the assignment. The fact is that, as a rule, the long side of the rectangle is called its length, and the short side is called its width. According to the terms of the assignment, the length of the rectangle is 14 centimeters; we got that the width of the rectangle is 2186 centimeters. If in the conditions of the task there would be one unit of length (any, for example, a unit), then the ending of the present solution would look as follows: “… 2 * (14 + x) = 44 or 14 + x = 22, whence x = 22 – 14 = 8. Therefore, the required area S is equal to (14 units) * (8 units) = 112 units ² “.