The length and breadth of a rectangular field are in the ratio of 5:3.The cost of fencing the field at₹25 per m is ₹3000.Find the dimension of the field
Answers
Given that the ratio of length of breadth of the rectangular field is 5 : 3.
∴ Length / Breadth = 5 / 3
Let length and breadth of the rectangular field be 5x and 3x respectively.
Now, length of the rectangular field = 5x
breath of the rectangular field = 3x
Area of the rectangular field = 2160 m^2
Length x Breadth = 2160 m^2
5x x 3x = 2160 m^2
15x^2 = 2160 m^2
⇒ x^2 = 2160 / 15 m^2
⇒ x^2 = 144 m^2
⇒ x^2 = ( 12 m )^2
⇒ x = 12 m
∴ Length of the rectangular field = 5x
= 5( 12 m )
= 60 m
Breadth of the rectangular field = 3x
= 3( 12 m )
= 36 m
Therefore length of the rectangular field is 60m and breadth of the rectangular field is 36m.
Perimeter of the rectangular field = 2( Length + Breadth )
∴ Perimeter = 2( 60m + 36m )
⇒ Perimeter = 2( 96 m )
⇒ Perimeter = 192 m
Hence, cost of fencing = area to be fenced( perimeter of rectanglee ) x rate of fencing per metre
cost of fencing = 192 m x Rs 350 / m
cost of fencing = Rs 67,200
Therefore the cost of fencing the rectangular field is Rs 67200.