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Fencing the compound of a house cost Rs. 4930. If the rate is Rs. 85 per metre, find the perimeter of the compound. If the breadth is 10 m, find its length.

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Last updated date: 14th Jul 2024
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Answer
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Hint: In this type of question we have to use the concept of perimeter of a particular shape. We know that the perimeter of a shape is nothing but the boundary that surrounds the shape. If we have to calculate the perimeter of a shape then we add all the sides of the shape. Also, we know that the total cost of fencing a compound can be calculated by using the formula, \[\text{Perimeter }\!\!\times\!\!\text{ Rate of fencing per meter}\]. Also we have to consider the formula of the perimeter of the rectangular compound which is given by, \[\text{2}\times \left( \text{length + breadth} \right)\].

Complete step by step answer:
Now, we have to find the perimeter of the compound if the total cost of fencing is Rs. 4930 and the rate of fencing is Rs. 85 per meter. Also we have to find the length if the breadth is 10 m.
As we know, the total cost of fencing of the compound is the product of the perimeter of the compound and the rate of fencing per meter.
\[\Rightarrow \text{Total cost of fencing the compound = Perimeter }\!\!\times\!\!\text{ Rate of fencing per meter}\]
\[\begin{align}
  & \Rightarrow Rs.4930=\text{ Perimeter }\times \text{ }Rs.85\text{ per meter} \\
 & \Rightarrow \text{ Perimeter = }\dfrac{Rs.4930}{Rs.85\text{ per meter}} \\
 & \Rightarrow \text{ Perimeter = 58 meter} \\
\end{align}\]
Hence, the perimeter of the compound is 58 meter.
Now, if the breadth of the compound is 10 m then we have to find the length.
As we know that the perimeter of rectangular compound is given by,
\[\Rightarrow \text{Perimeter of rectangular compound = 2}\times \left( \text{length + breadth} \right)\]
On substituting the values of the perimeter and the breadth we get,
\[\begin{align}
  & \Rightarrow 58=2\times \left( \text{length + }10 \right) \\
 & \Rightarrow \dfrac{58}{2}=\left( \text{length + }10 \right) \\
 & \Rightarrow 29=\left( \text{length + }10 \right) \\
 & \Rightarrow 29-10=\text{length} \\
 & \Rightarrow \text{19 = length} \\
\end{align}\]
Hence, the length of the compound is 19 meter.

Note: In this type of question we have to remember the formula of perimeter of given shape. Also first with the help of given total cost and rate per meter we have to calculate perimeter and then we will find the missing dimension of the given shape.