Question

the sides of a rectangular Park are in the ratio 3 : 2 if the area of is 1536 m*m square find the cost of fencing @ rupees 23.50 per metre​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bf{Given:-}\begin{cases}\sf{Area\:of\:park=1536m{}^{2}}\\ \sf{Sides\:are\:in\:ratio=3:2}\\ \sf{Cost\:of\: fencing\:1m= 23.50Rs}\end{cases}$

• Now first find the Side of rectangle then Th perimeter of park

$\bf\underline{\red{\:\:\:\:\:\:\:\:A T.Q:-\:\:\:\:\:\:\:\:}}$

• Let the Side of park be n

$\underline{\bigstar{\sf{Area\:of\: rectangle=Length\times breadth}}}$

• Side is 3n and 2n

$\sf\implies Area=l\times b\\ \\ \sf\implies 1536=2n\times 3n\\ \\ \sf\implies 1536=6n{}^{2}\\ \\ \sf\implies \cancel{\dfrac{1536}{6}}=n{}^{2}\\ \\ \sf\implies 256=n{}^{2}\\ \\ \sf\implies \sqrt{256}=n\\ \\ \sf\implies n=16$

• Now the sides of rectangle

$\sf\bullet side\\ \sf\bullet Breadth=2\times 16=32m\\ \sf\bullet Length=3\times 16= 48m$

$\boxed{\sf{\bigstar{Perimeter\:of\: rectangle=2(length+ breadth)}}}$

$\sf\implies Perimeter=2(48+32)\\ \\ \sf\implies Perimeter=2\times 80\\ \\ \sf\implies Perimeter=160m$

• Now find the cost of fencing

$\underline{\bigstar{\sf{Cost\:of\: fencing=Perimeter\times Rate}}}$

$\sf\implies Cost=160\times 23.50\\ \\ \sf\implies Cost=3760$

$\underline{\dag{\sf{\:\:Cost\:of\: Fencing=Rs3760}}}$

Answer 2

AnswEr :

Rs.3760

$\bf{\large{\underline{\underline{\tt{Given\::}}}}}}$

The sides of a rectangular park are in the ratio 3:2. If the area of is 1536m².

$\bf{\large{\underline{\underline{\tt{To\:find\::}}}}}}$

The cost of fencing Rs.23.50 per metre.

$\bf{\large{\underline{\underline{\rm{\red{Explanation\::}}}}}}$

Let the ratio be r

$\bf{We\:have}\begin{cases}\sf{Length\:of\:rectangular\:park=3r}\\ \sf{Breadth\:of\:rectangular\:park=2r}\\ \sf{Area\:=\:1536m^{2}}\\ \sf{Rate\:=\:Rs.23.50/m}\end{cases}}$

$\bf{\large{\underline{\underline{\tt{\green{A.T.Q\::}}}}}}}$

$\longrightarrow\tt{Area\:of\:rectangle\:=\:Length \times Breadth}$

$\longrightarrow\tt{3r\times2r\:=\:1536\:m^{2} }\\\\\\\\\longrightarrow\tt{6r^{2} \:=\:1536\:m^{2} }\\\\\\\\\longrightarrow\tt{r^{2} \:=\:\cancel{\dfrac{1536 }{6}} m^{2} }\\\\\\\\\longrightarrow\tt{r^{2} \:=\:256\:m^{2} }\\\\\\\\\longrightarrow\tt{r\:=\:\sqrt{256m^{2} } }\\\\\\\\\longrightarrow\tt{\green{r\:=\:16m}}$

$\bf{\large{\underline{\underline{\sf{\blacksquare{\sf{The\:sides\:of\:rectangular\:park\::}}}}}}}$

• Length = 3(16)m = 48 m
• Breadth = 2(16)m = 32 m

Now,

$\longrightarrow\tt{Perimeter\:of\:rectangular\:park\:=\:2(length+breadth)}\\\\\\\longrightarrow\tt{Perimeter\:=\:2(48m+32m)}\\\\\\\longrightarrow\tt{Perimeter\:=\:2(80m)}\\\\\\\longrightarrow\tt{\green{Perimeter\:=\:160\:m}}$

$\bf{\large{\boxed{\sf{\orange{The\:cost\:of\:fencing\::}}}}}}$

$\leadsto\rm{\blue{Perimeter\:of\:rectangular\:park\: \times\:Rate}}\\\\\\\leadsto\rm{Rs.\big(160\: \times\:23.50\big)}\\\\\\\leadsto\rm{\red{Rs.3760}}$

∴ The cost of fencing is Rs.3760.