The length and breadth of a rectangular are in the ratio 5:3 .If the cost of reaping the field at 85 paise per square metre is Rs 624.75 find the cost of fencing it at the rate of Rs 4per metre
To find the cost of fencing the rectangular field, we need to determine the length and breadth of the field and then calculate the perimeter.
Given that the length and breadth of the field are in the ratio 5:3, we can assume the length as 5x and the breadth as 3x (where x is a common multiple).
To find the value of x, we can use the given cost of reaping the field. We know that the cost of reaping at 85 paise per square meter is Rs 624.75.
Cost of reaping = area x rate
Area = length x breadth
Given cost of reaping = Rs 624.75
Rate = 85 paise = 0.85 Rupees
Length x Breadth = Area
Thus, 5x * 3x = 624.75 / 0.85
Simplifying it further:
15x^2 = 735
Divide both sides by 15:
x^2 = 49
Taking the square root on both sides:
x = √49
Therefore, x = 7
Now we know the value of x, we can find the length and breadth:
Length = 5x = 5 * 7 = 35
Breadth = 3x = 3 * 7 = 21
Next, we need to calculate the perimeter of the rectangular field:
Perimeter = 2 * (Length + Breadth)
Substituting the values:
Perimeter = 2 * (35 + 21) = 2 * 56 = 112 meters
Finally, we can calculate the cost of fencing at the rate of Rs 4 per meter:
Cost of fencing = Perimeter * Rate
Cost of fencing = 112 * 4 = Rs 448
Therefore, the cost of fencing the rectangular field at the rate of Rs 4 per meter is Rs 448.
length --- 5x m
width ----- 3x m
Area = 15x^2 m^2
15x^2 *.84 = 624.75
solve for x, and from there find the length and width.
Perimeter = 2length + 2 width
= 10x + 6x = 16x
cost of fencing = 4(16x) = 64x = .....