SOLUTION: A field 200 m by 150 m has a path of 2m running alonh the perimeter and cross path 3 m wide running in the centre vertically and horizontally. Find the cost of paving the pathways

Question 1038944: A field 200 m by 150 m has a path of 2m running alonh the perimeter and cross path 3 m wide running in the centre vertically and horizontally. Find the cost of paving the pathways at the rate of rupees 7 per square foot and the cost of sowing the crop in the field at the rate of 5 per rupees square foot?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Here is a sketch (not to scale) to visualize the problem:
If I had drawn it two scale, the paths would be too narrow to be visible.
The total area of the field is
.
Part of that (the pathways) needs to be paved, and the rest is where the crop will be planted.
The part where the crop will be planted is represented by the green rectangles.
The (horizontal) length of each of those rectangles is , and
their (vertical) width is .
So, in equations and in pictures .
<---><---><---><--->, and
<---><---><---><---><--->
So surface area of the part for sowing is
= area of the rectangle made by joining the 4 green rectangles.
Since the total area of the field is , the path area to be paved is
.
unfortunately, we have the surface areas in , but the costs for paving and sowing are given per square foot,
but is

, so
paving would cost , and
sowing would cost
.
The total cost of paving and sowing would be
.
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