Question

the length and breadth of a rectangular field are the ratio 3:2 it is the area of the field is 3456 m find the cost of fencing the field 4.50 per metre​

Answer 1

answer in the attachment

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Answer 2

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Given :-

• Ratio of the length and breadth of a rectangular field is 3 : 2

• Area of the field is 3456m²

To Find :-

• Cost of fencing the field at the rate of Rs. 4.50 per metre

Solution :-

First we will find the Length and breadth of the field

⟼ Let the length be 3x

⟼ Let the breadth be 2x

Formula used :-

⠀⠀⠀$\large\boxed{\sf\red{Area \: of \: rectangle = l × b }}$

where,

• l = Length of the field

• b = Breadth of the field

By substituting values :

$\sf{⟼3x \times 2x = {3456m}^{2} }$

$\sf{⟼6 {x}^{2} = 3456 {m}^{2} }$

$\sf{⟼ {x}^{2} = \dfrac{3456}{6} }$

$\sf{⟼ {x}^{2} = 576 }$

$\sf{⟼x = \sqrt{576} }$

$\sf{⟼x = 24}$

Therefore, The required measurements are,

✰ Length of the field = 3x = 3 × 24 = 72m

✰ Breadth of the field = 2x = 2 × 24 = 48m

Now,

⠀⠀⠀$\boxed{\sf\red{Perimeter \: of \: rectangle = 2( l + b )}}$

By substituting values,

$\sf{⟼2(72 + 48)m }$

$\sf{⟼2(120)m }$

$\sf{⟼240m }$

Hence, The perimeter of the rectangular field is 240m

➙ Cost of fencing the field at the rate of Rs. 4.50 per meter

$\sf{⟼240 \times 4.50}$

$\sf{⟼₹ 1080}$

Hence, The Cost of fencing the field at Rs. 4 per meter is ₹ 1080

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Additional information :-

⟼ Area of the square = ( side )²

⟼ Perimeter of the square = 4 × side

⟼ Area of the rectangle = l × b

⟼ Perimeter of the rectangle = 2( l + b )

⟼ Area of the circle = πr²

⟼ Perimeter of the circle = 2πr

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