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 of 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

Step-by-step explanation:

so let's start:

first of all we are given that the length is to breath ratio is 11:4

this mean that of we divide ans simplify length and breath then the ans will come 11/4

so we can conclude the original no.s must be divided by a common no. in order to obtain the simplified form .

so let that common no. be x

hence the original length is in terms of x is 11x and breath in terms of x is 4x

we know that by fencing we mean perimeter covering

so perimeter of the rectangle is 2(l+b)= 2(11x+4x)= 15x*2=30x m

we know that the cost per metre is 100 rs. (too costly)

we also know that total cost= quantity× cost per unit

total cost =Rs.75000

so 75000=30x*100

75000=3000x

x=75000÷3000

=25

hence,

length= 11×25=275m

breath=4×25=100m

HOPE IT HELPS

I WISH A GOOD HEALTH AND JOYFUL LIFE TO EVERYONE WHO IS READING THIS AND TO THOSE ALSO WHO ARE NOT. MAY GOD BLESS YOU.

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