Question

the cost of fencing a rectangular Park at rupees 28.50 per metre is rupees 3648 find its length and breadth if they are in ratio 5:3​

Answer 1

Answer:

$\bold\red{Length=40\:m}$

$\bold\red{Breadth=24\:m}$

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Let's take length as 5x and breadth as 3x

Now:-

$\longrightarrow\tt Perimeter = 2(length + breadth)$

$\longrightarrow\tt Perimeter = 2(5x+3x)\:m$

$\longrightarrow\tt Perimeter = 16x\:m$

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According to question:-

$\longrightarrow\tt Now,Perimeter=\frac{Cost}{Rate}$

$\longrightarrow\tt Perimeter=\frac{3648}{28.50}$

$\longrightarrow\tt Perimeter=128\:m$

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Now, 16x = 128 m

$\longrightarrow\tt x =\frac{128}{16}$

$\longrightarrow\tt x = 8\:m$

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D i m e n s i o n s :-

Length = 5x = 5 × 8 = 40 m

Breadth = 3x = 3 × 8 = 24 m

So,length is 40m and breadth is 24 m

#Answerwithquality #BAL

Answer 2

AnswEr :

$\bf{ Given}\begin{cases}\text{Cost of Fencing = Rs. 3648}\\\text{Rate of Fencing = Rs. 28.50 @metre}\\ \text{Length : Breadth = 5 : 3}\\\text{Find Dimensions of Park.} \end{cases}$

Let the Length be 5n, and Breadth be 3n.

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.5,2){\mathsf{\large{3n}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{5n}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

• Let's Head to the Question Now :

$\longrightarrow \tt Cost = Perimeter \times Rate \\ \\\longrightarrow \tt 3648 = Perimeter \times 28.50 \\ \\\longrightarrow \tt \dfrac{3648 \times 10}{285} = Perimeter \\ \\\longrightarrow \tt \dfrac{36480}{285} = Perimeter$

$\begin{array}{r|l} &\sf 1\:2\:8\\\cline{1-2} 285& 3\: 6\:4\:8\:0\\ &2\:8\:5\: \\ \cline{2-2} & \quad7\:9\:8\\&\quad5\:7\:0\\\cline{2-2} &\quad\:\:\:2\:2\:8\:0\\&\quad\:\:\:2\:2\:8\:0\\\cline{2-2}&\quad \:\boxed{0\:0\:0\:0}\end{array}$

$\longrightarrow \tt Perimeter = 128\:m \\ \\\longrightarrow \tt2(Length + Breadth) = 128\:m \\ \\\longrightarrow \tt2(5n + 3n) = 128 \\ \\\longrightarrow \tt2 \times 8n = 128 \\ \\\longrightarrow \tt16n = 128 \\ \\\longrightarrow \tt n = \cancel\dfrac{128}{16} \\ \\\longrightarrow \blue{\tt n = 8}$

$\rule{300}{1}$

• D I M E N S I O N S :

◗ Length = 5n = 5(8) = 40 m

◗ Breadth = 3n = 3(8) = 24 m

⠀

∴ Length and Breadth of the Rectangluar Park will be 40m and 24m respectively.

#answerwithquality #BAL