Question

The ratio of the two adjacent sides of a parallelogram is 5 : 8. Find all the sides of the prallelogram if its perimeter is 52 cm.​

Answer 1

Given that, the ratio of the two adjacent sides of a parallelogram is 5:8. So, let the two adjacent sides of the ||gm are 5x and 8x respectively.

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

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• Perimeter of the Parallelogram is 52 cm.
• And, we know that the opposite sides of parallelogram are equal and opposite.

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Therefore,

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$:\implies\sf 5x + 8x + 5x + 8x = 52 \\\\\\:\implies\sf 26x = 52 \\\\\\:\implies\sf x = \cancel\dfrac{52}{26}\\\\\\:\implies{\underline{\boxed{\sf{x = 2}}}}$

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Hence,

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• First side, 5x = 5(2) = 10 cm
• Second side, 8x = 8(2) = 16 cm

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$\therefore{\underline{\sf{Hence, \;sides\;of\;||^{gm}\;are\;\bf{10cm, 16cm, 10cm \;\&\;16cm\; respectively }.}}}$

Answer 2

Given :-

• Ratio of sides = 5:8
• Perimeter = 52 cm

To Find :-

Sides

Solution :-

Let the sides be 5x and 8x

Now,

$\sf Perimeter = 2(l + b)$

52 = 2(5x + 8x)

52 = 2(13x)

52 = 26x

x = 52/26

x = 2

Sides are

5(2) = 10 cm

5(2) = 10 cm

8(2) = 16 cm

8(2) = 16 cm