The length and breadth of a rectangular field are in the ratio 3 : 2. If the area of the field is 3456 m²,then the cost of fencing the field at 3.50 per metre is:

Given:

Length and breadth ratio = 3:2

Area of the field = 3456 m²

Cost of fencing = ₹3.50 per meter

Formula used:

Area rectangle = Length × Breadth

Calculation:

Let the length of the field be 3x and the breadth be 2x. Using the formula for area:

3456 = 3x × 2x

⇒ 3456 = 6x²

⇒ x² = 3456 / 6

⇒ x² = 576

⇒ x = √576 = 24

So, the length of the field = 3x = 3 × 24 = 72 meters, and the breadth of the field = 2x = 2 × 24 = 48 meters.

Perimeter = 2 × (Length + Breadth)

Perimeter = 2 × (72 + 48) = 2 × 120 = 240 meters

Cost of fencing = Perimeter × Cost per meter

Cost of fencing = 240 × 3.50 = ₹840

The cost of fencing the field is ₹840.