Final answer:
The length of the plot is 8m and the breadth is 8m.
Step-by-step explanation:
Let's assume the length of the plot is L and the breadth is B.
The perimeter of a rectangle is calculated using the formula P = 2(L + B), where P is the perimeter, L is the length, and B is the breadth.
According to the problem, 2(L + B) = 32. Solving this equation, we get L + B = 16.
If the length increases by 2m and the breadth decreases by 1m, the new length would be L + 2, and the new breadth would be B - 1.
We know that the new perimeter also remains the same. So, 2(L + 2 + B - 1) = 32.
Simplifying the above equation, we get L + B = 15.
Now we have two equations: L + B = 16 and L + B = 15. By substituting one equation into the other, we find that L = 8m and B = 8m.
Therefore, the length of the plot is 8m and the breadth is 8m.
Learn more about Calculating the dimensions of a rectangular plot of land