Question
A rectangular field is $240\ m$ long and $180\ m$ broad. In one corner a farm house is built on a square plot of side $40\ m$. Find the area of the remaining portion and the cost of fencing the open sides$ Rs.25$ per $m.$
✓
Answer
The area of a rectangle with length $I$ and breadth $b = A = I \times b$
The area of a rectangle with length $240\ m$ and breadth $180\ m$
$= 240 \times 180$
$= 43200\ m^2$
The area of a square plot with side 40m on which the farmhouse is made
$= 402$
$= 1600\ m^2$
The area of the remaining plot
$= 43200 - 1600$
$= 41600\ m^2$
The perimeter of a rectangle with length $I$ and breadth $b=P=2(I+b)$
The perimeter of a rectangle with length $240\ m$ and breadth $180\ m$
$= P$
$= 2(240 + 180)$
$= 840$
The boundary to be fenced
$= 840 - 2 \times 40$
$= 760$
The cost of fencing $1\ m = Rs.25$
$\Rightarrow$ The cost of fencing $760\ m$
$= Rs.25 \times 760$
$= Rs.19000.$
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