Question

the length and breadth of a rectangular field are in the ratio 5 is to 3 the area of the field is 2160 square metre if a fence is to be made @ rupees 350 per metre how much will it cost

Answer 1

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Answer 2

Question:

• The length and breadth of a rectangular field are in the ratio 5:3 the area of the field is 2160m² if a fence is to be made Rs. 350 per metre how much will it cost?

Given:

• Ratio of length and breadth of a rectangular park is 5:3. & Area of park is 2160m².

To find:

• Dimensions of rectangular park?
• The cost of Fencing?

⠀

Solution:

❍ Let's consider length and breadth of rectangular park be 5x and 3x.

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Required Formula:

$\:{\underline{\boxed{\frak{Area_{\:(rectangle)} = Length \times Breadth}}}} \color{navy}\bigstar$

• Let's Solve⠀⠀⠀⠀

$\begin{gathered}\bf{\maltese}\:{\underline{\frak{ \color{orange}{Putting\:given\:values\:in\:formula,}}}}\\\\\\ :\implies\sf 2160 = 5x \times 3x\\\\\\ :\implies\sf 2160 = 15x^2\\\\\\ :\implies\sf x^2 = \cancel{\dfrac{2160}{15}}\\\\\\ :\implies\sf x^2 = 144\\\\\\ :\implies\sf \sqrt{x^2} = \sqrt{144} \\\\\\ :\implies{\underline{\boxed{\frak{{x = 12}}}}}\pink\bigstar\\\\\end{gathered}$

Therefore,

$\sf \: Length \: of \: rectangular \: park, 5x=5(350) = \textsf{ \textbf{1750m}}$

$\sf \: Breadth \: of \: rectangular \: park, 3x=3(350)= \textsf{ \textbf{1050m}}$

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$\:{\underline{\sf{Hence,\:dimensions\:of\:rectangular\:park\:are\textsf{ \textbf{1750\:m}}\: {and}{\textsf{ \textbf {1050\:m}}}\: \sf{respectively}.}}}$

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