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Question
A rectangular grassy plot is 112 m long and 78 m broad. It has a gravel path 2.5 m wide all around it on the side. Find the area of the path and the cost of constructing it at Rs 4.50 per square metre.
Solution
Given:
The length of a rectangular grassy plot is 112 m and its width is 78 m.
Also, it has a gravel path of width 2 . 5 m around it on the sides.
Its rough diagram is given below:
Length of the inner rectangular field \[= 112 - (2 \times 2 . 5) = 107 m\]
The width of the inner rectangular field \[= 78 - (2 \times 2 . 5) = 73 m\]
∴ Area of the path = (Area of the rectangle with sides 112 m and 78 m) - (Area of the rectangle with sides 107 m and 73 m
\[ = (112 \times 78) - (107 \times 73)\]
\[ = 8736 - 7811\]
\[ = 925 m^2 \]
Now, the cost of constructing the path is Rs 4 . 50 per square meter.
∴ Cost of constructing the complete path = 925 x 4 . 50 = Rs 4162.5
Thus, the total cost of constructing the path is Rs 4162.5
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