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The length and breadth of a rectangular field are in the ratio 9: 5. If the area of the field is 14580 square meters, find the cost of surrounding the field with a fence at the rate of 3.25 per meter.
Given :
The length and breadth of a rectangular field are in the ratio 9:5.
Area of the field $=14580$ sq m.
Cost of fencing per meter $=₹3.25$.
To do :
We have to find the cost of fencing the rectangular field.
Solution :
Let the length and breadth of the field be 9x and 5x respectively.
Area of the field $=14580$ sq.m.
We know that,
The area of a rectangle of length l and breadth b is $l \times b$.
Therefore,
Area of the field$=(9x)\times (5x)$
$14580 = 45 x^2$
$\frac{14580}{45} = x^2$
$324 = x^2$
$x = 18$
So, length (l)$=9 (18) = 162 m$
Breadth(b)$=5(18) =90 m$
The perimeter of the rectangle $=2(l+b)$
$= 2(162+90) = 2(252) = 504$
Cost of fencing the field $=$ Perimeter $\times$ Cost of fencing per meter
$ = 504 \times 3.25 = 1638$
Therefore, the total cost of fencing the field is ₹1638.