Question

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs. 100 per metre it will cost the village panchayat Rs. 75000 to fence the plot. What are the dimensions of the plot ?

Answer 1

Given:

• Ratio of length and breadth of the park = 11:4
• Rate cost to fence per metre = Rs. 100
• Total amount cost to fence the plot = Rs. 75000

To Find:

The dimensions of the plot.

Solution:

Let us consider the length of the rectangular plot to be 11x and breadth be 4x

As we know,

Rate of fencing per metre = Rs. 100

Total amount cost to fence the plot = Rs. 75000

Then,

Perimeter of the plot = $2(l+b)=2(11x+4x)=2 \times 15x=30x$

Total amount of fencing = $(30x \times 100)$

According to the question,

$(30x \times 100)=75000\\\implies 3000x=75000$

Now, finding the value of x

$\implies x=\frac{75000}{3000} \\\implies x=25$

Therefore,

Length of the plot = $11x=11 \times 25 = \boxed{275 \: m}$

Breadth of the plot = $4x=4 \times 25 = \boxed{100 \: m}$

Thus, the length of the plot is 275 m, and the breadth is 100 m

Answer 2

Given:

•  The Length and Breadth of a rectangular plot are in the ratio of  11:4. & the rate of ₹100 per m it'll cost ₹75000 to fence the plot.

To find: 

• The dimensions of the plot?

Solution:

❍ Let's say, that the Length and Breadth of the plot be 11x and 4x respectively.

 PERIMETER:

Fencing of the plot requires four sides of the plot. Therefore, we've to find out the perimeter of the rectangular plot.

As we know that, Perimeter is Given by sum of its all sides. i.e. (a + b + c + d). So, Let's Solve —

⠀

$\begin{gathered}:\implies\sf Perimeter = 11x + 4x + 4x + 11x\\\\\\:\implies\sf Perimeter = 22x + 8x\\\\\\:\implies \underline {\boxed {\frak{ Perimeter = 30x}} } \blue\bigstar\\\\\end{gathered}$

• Perimeter is 30x.

⠀

Now,

Cost of Fencing

At the rate of 100 per metre, it'll cost the village to fence the rectangular plot at ₹75000.

Required Formula:

$\begin{gathered}\;\underline{\boxed{ \frak{\sf{ \color{navy}{Cost_{\;(fencing)} = Perimeter \times Rate}}}}} \ \orange\bigstar\\\\\end{gathered}$

$\begin{gathered}:\implies\sf 75000 = 30x \times 100 \\\\\\:\implies\sf 75000 = 3000x\\\\\\:\implies\sf x = \cancel\dfrac{75000}{3000}\\\\\\:\implies\underline{\boxed{\frak{{x = 25}}}} \pink\bigstar\end{gathered}$

Therefore,

• Length of the plot, 11x = 11(25) = 275 meters
• Breadth of the plot, 4x = 4(25) = 100 meters

4x = 4(25) = 100 meters⠀

${\underline{\textsf{Hence, the dimensions of the rectangular plot are \textbf{275 m, 100 m} respectively.}}}$

Thank you!!

@itzshivani