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The diogonals of a rhombus are …

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The diogonals of a rhombus are in the ratio 3:4 , and the area is 54 cm sq . Find the side of the rhombus.

Posted by Sundram Jha 5 years ago

CBSE > Class 08 > Mathematics

1 answers

Gaurav Seth 5 years ago

Let one diagonal = 3X, then other diagonal will be= 4X

Area of Rhombus = d₁*d₂/2 = 54 cm² (given)

or 3X * 4X /2= 54 cm²

or 6 X² =54cm²

or X = Sqrt (54/6) =3 cm

Therefore d₁ = 9 d₂ =12

As diagonals are perpendicular bisector of each other

Side of a rhombus = Sqrt { (d₁/2)²+(d₂/2)²}

side of rhombus = sqrt{(9/2)²+(12/2)²} = Sqrt ( 81/4 + 144/4)= Sqrt(225/4)

or Side = 15 / 2 = 7.5 cm (Ans)

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