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 75000 to fence the plot. What are the dimensions of
the plot?
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Answer:
Step-by-step explanation:
let the length be 11x
let the breadth be 4x
perimeter of rectangle= 2(l+b)
= 2(11x+4x)
= 2* 15x {11x+4x= 15x}
= 30x (2*15x=30x}
cost of fencing per metre= 100 rs
total cost= 75000rs
perimeter = 75000/100
=750 m
according to question-
30x = 750m
x = 750/30
x= 25 m
length = 11*25 = 275 m
breadth = 4*25 = 100 m
Appropriate Question:
Given:
To find:
Solution:
❍ Let's say, that the Length and Breadth of the plot be 11x and 4x respectively.
PERIMETER:
As we know that, Perimeter is Given by sum of its all sides. i.e. (a + b + c + d). So, Let's Solve —
⠀
[tex]\begin{gathered}:\implies\sf Perimeter = 11x + 4x + 4x + 11x\\\\\\:\implies\sf Perimeter = 22x + 8x\\\\\\:\implies \underline {\boxed {\frak{ Perimeter = 30x}} } \blue\bigstar\\\\\end{gathered}[/tex]
⠀
Now,
Cost of Fencing
Required Formula:
[tex]\begin{gathered}\;\underline{\boxed{ \frak{{ \color{navy}{Cost_{\;(fencing)} = Perimeter \times Rate}}}}} \ \orange\bigstar\\\\\end{gathered}[/tex]
[tex]\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}[/tex]
Therefore,
⠀
[tex]{\underline{\textsf{Hence, the dimensions of the rectangular plot are \textbf{275 m, 100 m} respectively.}}}[/tex]
Thank you!!
@itzshivani