the lenght of a rectangular field is thrice its breadth. if the area of field is 7500 m square, find the cost of fencing the field at the rate of RS 10 per meter
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To find the cost of fencing the field, we first need to find the dimensions of the rectangular field.
Let's assume that the breadth of the field is 'x' meters. According to the given information, the length of the field is three times the breadth, so the length would be '3x' meters.
We can use the formula for the area of a rectangle to find the value of 'x':
Area = Length × Breadth
Given, the area of the field is 7500 square meters:
7500 = 3x × x
Simplifying the equation:
7500 = 3x^2
Now, let's solve this quadratic equation for 'x':
Divide both sides of the equation by 3:
2500 = x^2
Taking the square root of both sides of the equation:
√2500 = √(x^2)
Simplifying:
50 = x
So, the breadth of the field is 50 meters.
Now, let's find the length of the field:
Length = 3 × Breadth
Length = 3 × 50
Length = 150 meters
The dimensions of the rectangular field are 150 meters (length) and 50 meters (breadth).
To find the cost of fencing, we need to calculate the perimeter of the field (which is the total length of the fence needed).
Perimeter = 2 × (Length + Breadth)
Perimeter = 2 × (150 + 50)
Perimeter = 2 × 200
Perimeter = 400 meters
The cost of fencing the field at a rate of RS 10 per meter is calculated by multiplying the perimeter by the cost per meter:
Cost of fencing = Perimeter × Cost per meter
Cost of fencing = 400 × RS 10
Cost of fencing = RS 4000
Therefore, the cost of fencing the field at the rate of RS 10 per meter would be RS 4000.
area=LW=2w^2
7500=2w^2 solve for w, then solve for L
cost=:(2L+2W)10