Question

b) The area of a rectangular park is 2160 square metre. If the length and the breadth of the park are

in the ratio 5 : 3. Find the dimension of the park.




Mainly find the dimension of the park
Ans. Fast​

Answer 1

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

Need to find: Dimensions of rectangular park?

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

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As we know that,

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$\star\:{\underline{\boxed{\frak{Area_{\:(rectangle)} = Length \times Breadth}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 2160 = 5x \times 3x\\\\\\ :\implies\sf 2160 = 15x^2\\\\\\ :\implies\sf x^2 = \cancel{\dfrac{2160}{15}}\\\\\\ :\implies\sf x^2 = 144\\\\\\ :\implies\sf \sqrt{x^2} = \sqrt{144} \\\\\\ :\implies{\underline{\boxed{\frak{\purple{x = 12}}}}}\:\bigstar$

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Therefore,

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

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$\therefore\:{\underline{\sf{Hence,\:Dimensions\:of\:rectangular\:park\:is\:\bf{60\:m}\: \sf{and}\: \bf{36\:m}\: \sf{respectively}.}}}$

Answer 2

Given :-

Area of park = 2160 sq. m

Ratio of length and breadth = 5:3

To find :-

Length and breadth

Solution :-

We know that

Area = Length * Breadth

Let the angle be 5x and 3x

$\sf \implies 2160 = 5x \times 3x$

$\sf \implies 2160 = 15x^{2}$

$\sf \implies \dfrac{2160}{15} = x^{2}$

$\sf \implies 144 = x^{2}$

$\sf \implies\sqrt{144} = x$

12 = x

5(12) = 60 m

3(12) = 36 m