Question

A rectangular plot measures 125 m by 78 m. It has gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at Rs 75 per m².

Answer 1

The plot with the gravel path is shown in the figure.


Area of the rectangular plot = $l\times b$
Area of the rectangular plot = $125\times 78=9750{\mathrm{m}}^2$
Length of the park including the path = 125 + 6 = 131 m
Breadth of the park including the path = 78 + 6 = 84 m
Area of the plot including the path
$$\begin{gathered} =131\times 84 \\ =11004{\mathrm{m}}^2 \end{gathered}$$

Area of the path = $11004-9750$
= 1254 m²
Cost of gravelling 1 m² of the path = Rs 75
∴ Cost of gravelling 1254 m² of the path = $1254\times 75$
= Rs 94050