In exchange of a square plot one of whose sides is 84 m,

Given:

Side of the square plot $=84 \mathrm{~m}$

Now, the man wants to exchange it with a rectangular plot of the same area with length 144 .

Area of the square plot $=84 \times 84=7056 \mathrm{~m}^{2}$

$\therefore$ Area of the rectangular plot $=$ Length $\times$ Width

$7056=144 \times$ Width

$\Rightarrow$ Width $=\frac{7056}{144}=49 \mathrm{~m}$

Hence, the width of the rectangular plot is $49 \mathrm{~m}$.