Question

The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m².

Answer 1

Ratio in length and breadth of a rectangular piece of land = 5 : 3

Cost of fencing = ₹9600

And rate = ₹24 per m

Perimeter =`"Total cost of fencing"/"Rate per m"`

= `9600/24`

= 400 m

Let length = 5x

Then breadth = 3x

∴ Perimeter = 2(l + b)

400 = 2 × (5x + 3x)

∴ 16x = 400

x = `400/16=25`

(i) ∴ Length of land = 5x = 5 × 25 = 125 m

and breadth = 3x = 3 × 25 = 75 m

(ii) Area = l × b

= 125 × 75 = 9375 m²

(iii) Cost of levelling at rate ₹60 per m²

= ₹60 × 9375 m² = ₹5,62,500