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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.

Last updated date: 14th Jul 2024
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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, $\text{2}\times \left( \text{length + breadth} \right)$.

$\Rightarrow \text{Total cost of fencing the compound = Perimeter }\!\!\times\!\!\text{ Rate of fencing per meter}$
\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}
$\Rightarrow \text{Perimeter of rectangular compound = 2}\times \left( \text{length + breadth} \right)$
\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}