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 100 per metre it will
cost the village panchayat 75000 to fence the plot. What are the dimensions of
the plot?
​

Answer 1

Let the common ratio between the length and breadth of the rectangular plot be x. Hence, the length and breadth of the rectangular plot will be 11x m and 4x m respectively.

Perimeter of the plot = 2 (Length + Breadth)

= [ 2 (11x + 4x) ] m = 30x m

It is given that the cost of fencing the plot at the rate of Rs 100 per metre is Rs 75, 000.

∴ 100 × Perimeter = 75000

100 × 30x = 75000

3000x = 75000

Dividing both sides by 3000, we obtain

x = 25

Length = 11x m = (11 × 25) m = 275 m

Breadth = 4x m = (4 × 25) m = 100 m

Hence, the dimensions of the plot are 275 m and 100 m respectively.

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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:

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

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

Therefore,

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

⠀

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

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@itzshivani