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Question

A rhombus has one diagonal double the other. If the area of rhombus is kcm2. then the length of its side is

A
5k4cm
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B
5k4cm
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C
5k4cm
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D
k54
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Solution

The correct option is C 5k4cm
Let the length of one diagonal be a,
The length of other diagonal will be 2a

We know,
Area of Rhombus=12d1×d2
=12a×2a=k
=a=k ----(i)

As diagonals intersect each other at right angles,
Let the side of rhombus be p

Now,
p2=d122+d222 -- Pythagoras Theorem.

p2=a24+a2=5a24

p=5a24
p=5k4 by (i)

Hence option C is correct answer.

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