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In a parallelogram, two sides are of length 5 cm and 10 cm respectively while the ratio of two diagonals of the parallelogram is 1 : 3, then what is the difference between the length of both the diagonals of the parallelogram?

In a parallelogram, two sides are of length 5 cm and 10 cm respectively while the ratio of two diagonals of the parallelogram is 1 : 3, then what is the difference between the length of both the diagonals of the parallelogram? Correct Answer 10 cm

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Let the length of sides of parallelogram be a and b respectively and length of diagonals of the parallelogram is e and f respectively.

Suppose e = x and f = 3x

According to Euler's quadrilateral theorem :

2a2 + 2b2 = e2 + f2

2 × 52 + 2 × 102 = x2 + (3x)2

50 + 200 = 10x2

x2 = 25

x = 5

Required difference = 3x – x = 2x = 10 cm

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