Question

The ratio of two sides of a parellelogram is 2:3 and its area is 96cm². The sides are

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Ratio of length and breadth = 2 : 3
• Area = 96cm²

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Length of the sides = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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$\sf{\red{\boxed{\bold{area = length \times breadth}}}}$

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• let the 2 sides be 2x and 3x

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$\sf :\implies\: {\bold{ 96 = 2x \times 3x}}$

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$\sf :\implies\: {\bold{ 6x^2 = 96 }}$

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$\sf :\implies\: {\bold{ x^2 = \dfrac{96}{6}}}$

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$\sf :\implies\: {\bold{ x^2 = 16}}$

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$\sf :\implies\: {\bold{ x =\sqrt{16}}}$

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$\sf :\implies\: {\bold{ x =\sqrt{2\times 2 \times 2 \times 2 }}}$

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$\sf :\implies\: {\bold{ x = 2\times 2}}$

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$\sf :\implies\: {\bold{ x = 4}}$

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• putting value of x in the sides

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2x = 2 × 4 = 8cm

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3x = 3 × 4 = 12cm

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Two sides of the parallelogram are 8cm and 12cm

Answer 2

QUESTION

The ratio of two sides of a parellelogram is 2:3 and its area is 96cm². The sides are

TO FIND

side =?

GIVEN

●Ratio of sides =2:3

●Area = 96cm^2

SOLUTION

let the sides be 2x and 3x

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$\sf \: {\bold{ 96 = 2x \times 3x}} \\ </p><p></p><p>⠀⠀⠀</p><p>\sf \: {\bold{ 6x^2 = 96 }} \\ </p><h3></h3><p>⠀⠀⠀⠀</p><p></p><p>\sf \: {\bold{ x^2 = \dfrac{96}{6}}} \\ </p><p>⠀⠀⠀⠀</p><p></p><p>\sf \: {\bold{ x^2 = 16}} \\ </p><p>\sf :\: {\bold{ x =\sqrt{16}}} \\ </p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf \: {\bold{ x =\sqrt{2\times 2 \times 2 \times 2 }}} \\ </p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf \: {\bold{ x = 2\times 2}} \\ </p><p></p><p>⠀⠀⠀⠀</p><p></p><p>\sf \: {\bold{ x = 4}} \\ </p><p></p><p>⠀⠀⠀⠀$

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$\large{ \sf \underline{ \blue{ ╬ \: substituting \: the \: value \: of \: x \: ╬}}}$

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☞2x = 2 × 4 = 8cm

☞3x = 3 × 4 = 12cm