Question

The ratio of two sides of a parallelogram is 2 : 5 and its perimeter is 70 cm. Find the sides of a parallelogram.

Answer 1

GivEn:

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• The ratio of two sides of a parallelogram is 2 : 5.
• Perimeter of parallelogram = 70 cm

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To find:

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• Sides of parallelogram?

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Solution:

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☯ Let two adjacent sides of parallelogram be 2x and 5x.

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⋆ Refrence of image is shown in diagram:

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`\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\put(0.7,2.5){\sf 2x}\put(3,0.5){\sf 5x}\end{picture}`

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`\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\`

• Perimeter of parallelogram = 70 cm

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`\dag\;{\underline{\frak{We\;know\;that,}}}\\ \\`

`\star\:{\boxed{\sf{\purple{Perimeter_(\;(parallelogram)) = 2 * (sum\:of\: adjacent\:sides)}}}}\\ \\`

`:\implies\sf 2 * (2x + 5x) = 70\\ \\`

`:\implies\sf 2 * 7x = 70\\ \\`

`:\implies\sf 14x = 70\\ \\`

`:\implies\sf x = \cancel{ (70)/(14)}\\ \\`

`:\implies{\boxed{\sf{\pink{x = 5}}}}\;\bigstar\\ \\`

Therefore,

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• 2x = 2 × 5 = 10 cm

• 5x = 5 × 5 = 25 cm

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`\therefore` Hence, Adjacent sides of parallelogram are 10 cm and 25 cm.

Answer 2

Let the ratio constant be x. Therefore two adjacent sides of the parallelogram are 2x cm and 5x cm in length.

Then, perimeter = 2 (sum of the adjacent sides)

`= > 70 = 2(2x + 5x) \\ \: \: \: \: \: \: \: \: 70 = 2(7x) \\ \: \: \ \: \: \: \: \: 35 = 7x \\ \: \: \: \: \: \: \: \: \: \: x = 5`
Hence, the sides of the parallelogram are
2 × 5 cm = 10 cm
5 × 5 cm = 25 cm