Maths-

General

Easy

Question

# 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.

Hint:

### i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks/ wires to prevent livestock from getting away.

ii. Perimeter of a rectangle = 2 (length + breadth)

## 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.

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