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Question

If the rate of change of area of rhombus with respect to its side is equal to the side of the rhombus, then the angles of rhombus are

A
π3 and 2π3
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B
π4 and 3π4
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C
π6 and 5π6
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D
5π12 and 7π12
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Solution

The correct option is C π6 and 5π6
Let x be the side of the rhombus.
Let θ be an angle of the rhombus.
Then, area of rhombus is given by A=x2sinθ
dAdx=2xsinθ
But, dAdx=x
2xsinθ=xsinθ=12
θ=π6, 5π6

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