Question

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

Answer 1

Answer: (C)

Square

Let sides are $a$ and $b$ and $perimeter$=$2p$

$2(a+b)=2p$

$(a+b)=p$

$A=area=ab=a(p-a)=pa-a^2$

$\frac{dA}{da}=p-2a=0$

$2a=p$

$a=p/2$

$b=p/2$

hence

$a=b$ $\left(square\right)$