Question

6. The length and breadth of a rectangular field are in the ratio 3:2. if the area of
field is 34565 m. find the cost of fencing the field at Rs.3.50 per meter.​

Answer 1

Step-by-step explanation:

Let the length be 3x and breadth be 2x

Area of rectangular field = 34565

$3x \times 2x = 34565 \\ 6 {x}^{2} = 34565 \\ {x}^{2} = \frac{34565}{6} = 5760.83 \\ {x} = \sqrt{5760.83} = 75.90 \\ 3x = 3 \times 75.90 = 227.70 \\ 2x = 2 \times 75.90 = 151.80 \\ Perimeter \: of \: field \: = 2(227.70 + 151.80) \\ = 2 \times 379.50 \\ = 759 \: m \\ Total \: coat \: of \: fencing = 3.50 \times 759 \\ = 2656.50 \\ Hence, \: total \: cost \: of \: fencing \\ \: is Rs. \: 2656.50.$

Answer 2

Let the length of the field be 3x m

Then , it's breadth = 2x m.

So , Area of the field =( Length × Breadth ) sq. unit

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 2x × 3x)m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 6x²) m²

But , area = 3456m² ( given )

So, 6x² = 3456 =》x² = $\frac{3456}{6} = 576$

x = $\sqrt{576} = 24.$

So, Length = ( 3 × 24 ) m

⠀⠀⠀⠀⠀⠀⠀= 48 m

⠀⠀ Breadth = ( 2 × 24 )m

⠀⠀⠀⠀⠀⠀⠀⠀= 72 .

Then , Perimeter of field = 2( l + b)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 ( 48 + 72)m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 2 × 120 )m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 240 m .

Hence , the cost of fencing = Rs. ( 240 × 3.50 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= Rs. 840 ans.

$\huge\mathcal\color{teal}Hope\:it\:helps!!$

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