Question

The length and breadth of a rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at 24 per metre is 9600, find its length and breadth.​

Answer 1

Answer:

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Answer 2

Answer:

Given :

The length and breadth of a rectangular piece of land are in the ratio of 5 : 3.

The total cost of fencing it at 24 per metre is 9600.

To Find :

The length of land

The breadth of land

Solution :

First, we will find the perimeter of the land. As the rate of fencing and the cost of fencing is given. We can easily find its perimeter.

$\begin{gathered}\quad{\longrightarrow{\sf{Perimeter = \dfrac{Total \: cost \: of \: fencing }{Cost \: of \: fencing \: 24 \: per \: m}}}} \\ \\ {\longrightarrow{\sf{Perimeter = \dfrac{9600}{24}}}} \\ \\ {\longrightarrow{\sf{Perimeter = \cancel{\dfrac{9600}{24}}}}} \\ \\ {\longrightarrow{\sf{\underline{\underline{\red{Perimeter = 400 \: m}}}}}}\end{gathered}$

Hence, the perimeter of rectangular land is 400 m.

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Now, let the length and breadth of rectangular land be 5x and 3x and the perimeter of rectangular land is 400 m.

Now, according to the question :

$\begin{gathered}\quad{\longrightarrow{\sf{Perimeter = 2(length + breadth}}} \\ \\ {\longrightarrow{\sf{400= 2(5x + 3x)}}} \\ \\ {\longrightarrow{\sf{400= 2(8x)}}} \\ \\ {\longrightarrow{\sf{400= 16x}}} \\ \\ {\longrightarrow{\sf{x = \dfrac{400}{16}}}} \\ \\ {\longrightarrow{\sf{x = \cancel{\dfrac{400}{16}}}}} \\ \\ {\longrightarrow{\sf{\underline{\underline{\red{x = 25}}}}}}\end{gathered}$

Hence, the value of x is 25.

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Now, we know the value of x. So, finding the length and breadth of rectangular land :

• ✧ Length = 5x = 5×25 = 125 m.
• ✧ Breadth = 3x = 3×25 = 75 m.

Hence, the length and breadth of rectangular land is 125m and 75m.

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Learn More :

$\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}$

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