Question

Veer and Ayush together have purchased a rectangular land of area 648 m². They have decided to split it into two halves with a single straight line and the cost of fencing the common boundary is paid by Veer, then find the minimum possible cost incurred by Veer in fencing his half at the rate of Rs. 2/m?
1. Rs. 150
2. Rs. 200
3. Rs. 180
4. Rs. 144
5. Rs. 156

Answer 1

Correct Answer - Option 4 : Rs. 144

Given:

Area of the half part of land = 324 m²

Cost of fencing Veer’s Land = Rs. 2/m.

Concept Used:

Area of Rectangle = L × B

The perimeter of Rectangle = 2(L + B)

Cost of fencing for Veer’s Land = Rs. 2/m × Perimeter of Veer’s land.

Calculation:

Let the length and breadth of Veer’s part be L m and B m respectively

⇒ L × B = 324

For a minimum cost of fencing, the perimeter should be minimum, and it will be possible only

When L = B

⇒ L² = 324

⇒ L = 18 m

The perimeter of Veer’s land = 72 m

Cost of fencing for Veer’s Land = Rs. 2/m × Perimeter of Veer’s land.

⇒ Rs. 2 × 72

Cost of fencing = Rs. 144 

∴ The Cost of fencing for Veer’s Land is Rs. 144.