A large rectangular land plot with an area of 4320 square meters is initially divided into three smaller square plots by fencing parallel to its shorter side. However, a leftover area remains that cannot form a square. To cover this remaining area completely, three additional square plots are created by fencing parallel to the longer side of the original plot. After this, no land area is left unused. What are the dimensions of the original rectangular plot?

Explanation

Let the side length of the smaller square at one end be 'a'. Then, the side length of the larger square is 3a. The total area is composed of three small squares (each of area a²) plus three larger squares (each of area (3a)²), so total area = 3a² + 3(3a)² = 3a² + 27a² = 30a². Given the total area is 4320 m², we have 30a² = 4320, which simplifies to a² = 144, so a = 12 meters. The shorter side of the rectangle is 3a = 36 meters, and the longer side is 3 × (3a) + a = 10a = 120 meters. Therefore, the original plot measures 120 meters by 36 meters.