Question

What will be the cost of fencing a rectangular compound if the wire costs 20 rs per meter? Also, the area is $ 40 m^2$ and length = 2 × breadth?

Answer 1

Hint: Perimeter of rectangle is the total distance covered by the rectangle around its outside. We know that, perimeter of the rectangle is equal to 2 (length + breadth). We are given an area of a rectangle and also given \[length = 2 \times breadth\]. We know that the area of a rectangle is equal to \[length \times breadth\]. Solving this, we will get the value of breadth and substituting in the given expression we will get the value of length too. Also we are given that the cost of wire is 20 m square and using this we will get the final output.

Complete step-by-step answer:
Given that,
Area of rectangular compound = 40 m2
Also given that,
\[length = 2 \times breadth\] ---- (1)
The figure of the rectangle is given below:

Now,
Area of rectangle = 40
\[ \Rightarrow length \times breadth = 40\]
Substituting the value of length from equation (1), we will get,
\[ \Rightarrow 2 \times breadth \times breadth = 40\]
\[ \Rightarrow 2 \times breadt{h^2} = 40\]
\[ \Rightarrow breadt{h^2} = \dfrac{{40}}{2}\]
\[ \Rightarrow breadt{h^2} = 20\]
\[ \Rightarrow breadth = \sqrt {20} \]m
Next, we will substitute the this value of breadth in equation (1), we will get,
\[length = 2 \times breadth\]
\[ \Rightarrow length = 2 \times \sqrt {20} \]
\[ \Rightarrow length = 2\sqrt {20} \]m

Also, we will find the perimeter of rectangle as below:
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle.
Perimeter of rectangle
\[ = 2\left( {length + breadth} \right)\]
\[ = 2(2\sqrt {20} + \sqrt {20} )\]
\[ = 2(3\sqrt {20} )\]
\[ = 6\sqrt {20} \]
\[ = 6 \times 4.47\] \[\left( {\because \sqrt {20} = 4.47} \right)\]
\[ = 26.8\]m
Given that,
Rate of the wire is Rs20 per meter.
Thus,
Cost of fencing the rectangular compound
\[ = 26.8 \times 20\]
\[ = 536\]Rs
Hence, the total cost of fencing the rectangle compound is Rs 536.
So, the correct answer is “536 Rs”.

Note: Perimeter basically gives the length of the figure. A rectangle is a quadrilateral which has two pairs of parallel sides equal and all the four angles at the vertices are right angles. Area of rectangle is the region covered by the rectangle in a two-dimensional plane. The area of a rectangle depends on its sides. In short, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.