A rectangular grassy plot is 112 m long and 78 m broad.

Given:

The length of a rectangular grassy plot is $112 \mathrm{~m}$ and its width is $78 \mathrm{~m}$.

Also, it has a gravel path of width $2.5 \mathrm{~m}$ around it on the sides.

Its rough diagram is given below :

Length of the inner rectangular field $=112-(2 \times 2.5)=107 \mathrm{~m}$

The width of the inner rectangular field $=78-(2 \times 2.5)=73 \mathrm{~m}$

$\therefore$ Area of the path $=$ (Area of the rectangle with sides $112 \mathrm{~m}$ and $78 \mathrm{~m})$

- (Area of the rectangle with sides $107 \mathrm{~m}$ and $73 \mathrm{~m}$ )

$=(112 \times 78)-(107 \times 73)$

$=8736-7811$

$=925 \mathrm{~m}^{2}$

Now, the cost of constructing the path is Rs $4.50$ per square meter.

$\therefore$ Cost of constructing the complete path $=925 \times 4.50=\mathrm{Rs} 4162.5$

Thus, the total cost of constructing the path is Rs $4162.5$