The lengths of the diagonals of a rhombus are in the ratio 3:4. If the perimeter is 100 cm,find length of sides and the diagnols
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Answer:
30 cm, 40 cm, 25 cm
Step-by-step explanation:
Perimeter = 100 cm.
=> 4 * s = 100
=> s = 25 cm.
Length of diagonals are in ratio 3 : 4.
The diagonals of a rhombus bisect each other. Let the diagonals are 3x and 4x. Half of the length of the diagonals form a right-angled triangle with a side of the rhombus.
(3x/2)^2 + (4x/2)^2 = 25^2.
=> 9x^2/4 + 16x^2/4 = 625
=> 25x^2/4 = 625
=> 25x^2 = 2500
=> x^2 = 100
=> x = 10
Thus,
3x = 30 cm and 4x = 40 cm.
Hence,
Length of sides are 30 cm and 40 cm.
Length of the diagonals = 25 cm.
#Hope my answer has helped you.
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