Question

There is a narrow rectangular plot,reserved for a school, in mahuli village. The length and the breadth of the plot are in ratio 11:4. At the rate hundred rupees per meter. It will cost the village panchayat 75,000 rupees to fence the plot .what are the dimensions of the plot.​

Answer 1

Step-by-step explanation:

Let the length and breadth's common ratio: x in metre

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4x

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30x

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000∴100× Perimeter =75000

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000∴100× Perimeter =750003000x=75000

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000∴100× Perimeter =750003000x=75000x=25

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000∴100× Perimeter =750003000x=75000x=25Length =11×x=11×25=275 m

Let the length and breadth's common ratio: x in metre∴ Length :11x and Breadth :4xPerimeter ⇒2(l+b)=2(11x+4x)=30xAs per the question:Cost of fencing plot at rate of Rs.100 per meter is Rs.75000∴100× Perimeter =750003000x=75000x=25Length =11×x=11×25=275 mBreadth =4x,=4×25=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:

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

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

Therefore,

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

⠀

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

Thank you!!

@itzshivani