Question

The Length and breadth of a rectangular field are in the ratio 9:5. If the area of the field is 14850 square metre. Find the cost of Surrounding the field with a fence at the rate of 2 3.25 per mer​

Answer 1

Appropriate Question:-

The Length and breadth of a rectangular field are in the ratio 9:5. If the area of the field is 14850 square metre. Find the cost of Surrounding the field with a fence at the rate of 3.25 per square metre.

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Given:-

• Length and breadth of a rectangular field are in the ratio 9:5.

• Area of the Field is 14,850m².

To Find:-

• Cost of Surrounding the field with a fence at the rate of 3.25 per square metre.

Formula Used:-

• ${\boxed{\bf{\red{Area\:of\: Rectangle=Length \times Breadth}}}}$

• ${\boxed{\bf{\red{Perimeter\:of\: Square=2(l+b)}}}}$

Solution:-

Let the length and breadth be 9x and 5x.

Firstly,

$\sf :\implies\:Area\:of\: Field= Length \times Breadth$

$\sf :\implies\:14,850= 9x \times 5x$

$\sf :\implies\:14,850= 45x^2$

$\sf :\implies\:x^2=\dfrac{14,850}{45}$

$\sf :\implies\:x^2=330$

$\sf :\implies\:x=\sqrt{330}$

• Length = 9x = $\bf 9\sqrt{330}m$

• Breadth = 5x = $\bf 5\sqrt{330}m$

Now,

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

$\sf :\implies\: Perimeter\:of\: Field=2(9\sqrt{300}+5\sqrt{300})$

$\sf :\implies\: Perimeter\:of\: Field=2 \times 14\sqrt{300}$

$\sf :\implies\: Perimeter\:of\: Field=28\sqrt{300}m$

Finally,

Cost of Surrounding the field with a fence at the rate of 3.25 per square metre:-

$\sf :\implies\: 28\sqrt{300}\times 3.25$

$\sf :\implies\: 28\times 17.32\times 3.25$

$\sf :\implies\: Rs. 1,576.12$

Hence, Cost of Surrounding the field with a fence at the rate of 3.25 per square metre is Rs. 11,576.12.

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