A rectangular field has its length and breadth in the ratio 5 : 3. Its area is 3.75 hectares. Find the cost of fencing it at ~ 5 per metre.

The correct answer is: Final Answer:- ∴ The cost of fencing the given rectangle field is Rs. 4,000.

Step-by-step solution:-
For the given rectangle field, we are given that length : breadth = 5 : 3
Let x be the common factor
∴ length = 5x, breadth = 3x
1 hectare = 10,000 sq mt
∴ 3.75 hectares = 3.75 × 10,000 = 37,500 m2
Area of the given rectangular field = length × breadth
∴ 37,500 = 5x × 3x ............................................................. (From given information)
∴ 37,500 = 15 x2
∴ 37,500 / 15 = x2
∴ 2,500 = x2
∴ 50 = x .................................................................... (Taking square root both the sides)
∴ Length = 5x = 5 × 50 = 250 m
& Breadth = 3x = 3 × 50 = 150 m
We need to find the cost of fencing the field at Rs. 5 per mt.
Since fences are put on the boundaries of the field, we need to calculate the perimeter of the field to find the cost of fencing it
∴ Perimeter of the given field = 2 (length + breadth)
∴ Perimeter of the given field = 2 (250 + 150)
∴ Perimeter of the given field = 2 × 400
∴ Perimeter of the given field = 800 m
∴ cost of fencing the whole field (@ Rs. 5 per mt) = 800 m × Rs. 5/ mt
∴ cost of fencing the whole field (@ Rs. 5 per mt) = Rs. 4,000
Final Answer:-
∴ The cost of fencing the given rectangle field is Rs. 4,000.