Question

6. 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 3 75000 to fence the plot. What are the dimensions of
the plot?​

Answer 1

Answer:

Length = 1375 m & Breadth = 500 m

Step-by-step explanation:

Cost of fencing per metre = Rs. 100

{ For fencing, we need to find the perimeter of the plot }

Let the perimeter be x metre,

Cost of fencing x metre = x × 100 = Rs. 375000

                                       ⇒ x = 375000 / 100

                                       ⇒ x = 3750 m

∴ The perimeter of the plot is 3750 m.

Ratio of length to the breadth =

Length : Breadth = 11 : 4

Let the common ratio be y

Length = 11y  ;  Breadth = 4y

Perimeter of rectangle = 2( l + b )

3750 = 2 ( 11y + 4y )

3750 = 2 ( 15y )

3750 = 30y    or     30y = 3750

y = 3750 / 30

y = 125

Length = 11y = 11 × 125 = 1375 m

Breadth = 4y = 4 × 125 = 500 m

∴ The dimensions of the plot are 1375 m by 500 m

Answer 2

Appropriate 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 meter it will cost the village panchayat ₹75000 to fence the plot. what are the dimensions of the plot?

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