Question

The length & breadth of a rectangular field are in the ratio 6:4
Find length and breadth if the cost of fencing the field is at the rate
of Rs 80 per metre is Rs 16,000

Answer 1

Given:-

• Ratio of length and breadth of a rectangular field = 6 : 4
• Cost of fencing the field at the rate of Rs. 80 per metre = Rs. 16,000

To Find:-

• It's Length and Breadth

Formula Used:-

• Perimeter of Rectangle = 2(l+b)

• Cost of Fencing = Perimeter of field × Rate of fencing

Solution:-

Let the Length and Breadth be 6x and 4x respectively.

Using Formula,

$\sf :\implies Perimeter \:of \: Rectangle = 2(l+b)$

Putting Values,

$\sf :\implies Perimeter \:of \: Field = 2(6x+4x)$

$\sf :\implies Perimeter \:of \: Field = 2\times 10x$

$\sf :\implies Perimeter \:of \: Field = 20x$

Now,

$\sf :\implies \:Cost\: of \:Fencing = Perimeter \:of \:field \times Rate\: of \:fencing$

Putting values,

$\sf :\implies \:16,000 = 20x \times 80$

$\sf :\implies \:1,600x = 16,000$

$\sf :\implies \:x = \dfrac{16,000}{1,600}$

$\sf :\implies \:x = \dfrac{160}{16}$

$\sf :\implies {\underline{x = 10}}$

Now,

• Length = 6x = 6 × 10 = 60m

• Breadth = 4x = 4 × 10 = 40m

Hence The Length and Breadth of the rectangular field is 60m and 40m respectively.

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