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The area of a rectangle will be maximum ...

The area of a rectangle will be maximum for the given perimeter, when rectangle is a

A

parallelogram

B

trapezium

C

square

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that perimeter of a rectangle `S=2(x+y)`, where x and y are adjacent sides
`impliesy=(S-2x)/(2)`, Now area of rectangle,
`A=xy=(x)/(2)(S-2x)=(1)/(2)(Sx-2x^(2))`
Differentiating w.r.t., x of A, we get
`(dA)/(dx)=(1)/(2)(S-4x)=0becausex=(S)/(4) and y=(S)/(4)`
Again `(d^(2)A)/(dx^(2))=-ve`
Hence the area of rectangle will be maximum when rectangle is a square.
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