Question

If the area of a rectangular park is 2160 sq.m and the length and breadth of the park are in the ratio 5 : 3, then cost of fencing the park at Rs. 5 per metre is

Answer 1

Answer:

2000metre square

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Answer 2

Question:

• If the area of a rectangular park is 2160m² and the length and breadth of the park are in the ratio 5:3, then what is the cost of fencing the park at Rs.5 per metre?

Given:

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

To find:

• Dimensions of rectangular park?

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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⠀⠀⠀⠀

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

Therefore,

• Length of rectangular park, 5x=60m
• Breadth of rectangular park, 3x=36m

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$\:{\underline{\sf{Hence,\:dimensions\:of\:rectangular\:park\:are\textsf{ \textbf{60\:m}}\: {and}{\textsf{ \textbf {36\:m}}}\: \sf{respectively}.}}}$

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