The length and breadth of a rectangular field are in the ratio 5:3.The area of the field is 2160 sq.m.If a fence is to be made at the rate of rupees 350 per metre, how much will it cost?
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.
Here is your answer:-
Step 1 :
The length and breadth are in ratio 5 : 3
Let the ratio be 5 x : 3 x
such that length is 5 x and breadth is 3 x
Area is the product of length and breadth
Area = l b
==> Area = 2160 m²
Now 5 x * 3 x = 2160 m²
==> 15 x² = 2160 m²
==> x² = 2160 m² / 15
==> x² = 144 m²
==> x = 12 m
Step 2:
Thus the length is 5 x
==> 5 * 12 m
==> 60 m
Breadth is 3 x
==> 3*12 m
==> 36 m
Now fencing the field means that we need to find the perimeter
==> Perimeter is 2 ( l + b )
==> 2 ( 60 m + 36 m )
==> 2 * 96 m
==> 192 m
Step 3:
The cost of fencing is Rs 350 per metre
Hence for 192 m the cost is
==> Rs 350 * 192
==> Rs 67200
The cost of fencing the field is Rs 67200
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Hope it helps you