A big rectangular plot of area 4320m² is divided in to 3 square shaped smaller plots by fencing parallel to the smaller side of the plot. However, some area of land was still left as a square could not be formed. So, 3 more square shaped plots were formed by fencing parallel to the longer side of the original plot such that no area of the plot was left surplus. What was the dimensions of the original plot?

To find the correct dimensions, let the length of the rectangular plot be L and the width be W. The total area is L multiplied by W, which equals 4320 square meters. First, the plot is divided into 3 squares by fencing parallel to the smaller side W. This means three squares of size W by W are removed from the length. The length used for these squares is 3W. Since some land was left over, the original length L must be greater than 3W. The remaining area is a rectangle with dimensions W and L minus 3W. Next, this remaining area is divided into 3 smaller squares by fencing parallel to the longer side of the original plot. This means the side of these 3 new squares must be L minus 3W, and 3 such squares must fit exactly into the width W. Therefore, W equals 3 times the quantity L minus 3W. Solving this equation: W equals 3L minus 9W. 10W equals 3L. L equals 10W divided by 3. Now substitute this into the area formula: (10W / 3) multiplied by W equals 4320. 10W squared equals 12960. W squared equals 1296. W equals 36. If W is 36, then L is 4320 divided by 36, which equals 120. The dimensions are 120 m by 36 m, which matches Option C.