The perimeter of a rectangular plot is 84 m. If its length is decreased by 6 m and its breadth increased by 6 m, the plot becomes a square. Find the length of the plot.

Let the length be $x$ and the breadth $y.2(x+y)=84$ gives $x+y=42$, and $x-6=y+6$ gives $x-y=12$. Adding: $2x=54$, so $x=27$ and $y=15$. Check: $2(27+15)=84$, and 27 - 6 = 21 = 15 + 6. 15 m is the breadth; 21 m is the side of the square that is formed; 42 m is half the perimeter, that is length plus breadth.