Question

The length of a rectangular plot is \[20\] metres more than its breadth. If the cost of fencing the plot at \[26.50\] per metre is Rs.\[5300\], what is the length of the plot in metres?
A) \[40\]
B) \[50\]
C) \[120\]
D) Date inadequate
E) None of these

Answer 1

Hint: We have to find the length of the plot in metres. It is given that the expenses for fencing the plot per metre. To find that at first, we will consider the length of the plot in terms of the breadth. Then, using the formula of perimeter, we will find the perimeter. Then we can find the total cost. Equating the total cost with the given cost, we can find the length of the plot.

Complete step-by-step answer:
It is given that; the length of a rectangular plot is \[20\] metres more than its breadth. The cost of fencing the plot at \[26.50\] per metre is Rs.\[5300\].
We have to find the length of the plot.
Let us consider, the breadth of the rectangular plot is \[b\]. So, its length is \[b + 20\].
So, we get, the perimeter of the given rectangular plot is \[2(b + 20 + b)\] cm
Simplifying we get,
The perimeter is \[2(2b + 20)\] cm.
The cost of fencing the plot at \[26.50\] per metre.
So, the cost of fencing of the rectangular plot is Rs.\[2(2b + 20) \times 26.50\]
According to the problem,
$\Rightarrow$\[2(2b + 20) \times 26.50 = 5300\]
Simplifying we get,
$\Rightarrow$\[(2b + 20) = \dfrac{{5300}}{{26.50 \times 2}}\]
Simplifying again we get,
$\Rightarrow$\[(2b + 20) = 100\]
Simplifying again we get,
$\Rightarrow$\[2b = 80\]
Simplifying again we get,
$\Rightarrow$\[b = 40\]
So, the breadth of the rectangular plot is \[40\] cm.
Therefore, the length of the rectangular plot is \[40 + 20 = 60\] cm
Hence, the length of the rectangular plot is \[60\] cm.

$\therefore $ The correct option is E) None of these.

Note: The perimeter of a rectangle is the total length of all the sides of the rectangle.
The fence around the rectangular plot means the length of the fence is equal to the perimeter of the plot.
We know that the perimeter of a rectangular plot when the length and breadth is \[l\] and \[b\]respectively is \[2(l + b)\].
We can solve it by change the consideration of length and breath,
Let us consider, the length of the rectangular plot is \[l\]. So, its length is \[l - 20\].
So, we get, the perimeter of the given rectangular plot is \[2(l - 20 + l)\] cm
Simplifying we get,
The perimeter is \[2(2l - 20)\] cm.
The cost of fencing the plot at \[26.50\]per metre.
So, the cost of fencing of the rectangular plot is Rs.\[2(2l - 20) \times 26.50\]
According to the problem,
\[2(2l - 20) \times 26.50 = 5300\]
Simplifying we get,
\[(2l - 20) = \dfrac{{5300}}{{26.50 \times 2}}\]
Simplifying again we get,
\[(2l - 20) = 100\]
Simplifying again we get,
\[2l = 120\]
Simplifying again we get,
\[l = 60\]
So, the length of the rectangular plot is \[60\]cm.
Therefore, the breath of the rectangular plot is \[60 - 20 = 40\]cm