Question

if the measure of two adjacent sides of a parellelogram are in the ratio 2:3 and the perimeter of the parellelogram is 50cm.Find the lengths of the sides of the parallelogram.​

Answer 1

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

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Ratio of length and breadth = 2 : 3

Area = 96cm²

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

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Length of the sides = ??

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

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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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$\huge\bf{\bold{\green{\underline{\underline{Answer}}}}}$

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Two sides of the parallelogram are 8cm and 12cm