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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
In a school, an auditorium was used for its cultural activities.
The shape of the floor of the auditorium is rectangular with dimensions $x$ and $y$ $(x>y)$ and has fixed parameter $p$.
Based on the above information answer the following questions.
Maximum area of floor is:
Solution
From the given condition
$p=2(x+y)$
So
$x+y=\frac{p}{2}$
Area of rectangle
$A=xy$
Put
$y=\frac{p}{2}-x$
So
$A=x\left(\frac{p}{2}-x\right)$
$A=\frac{px}{2}-x^2$
To maximize area
$\frac{dA}{dx}=\frac{p}{2}-2x=0$
Hence
$x=\frac{p}{4}$
Then
$y=\frac{p}{2}-\frac{p}{4}=\frac{p}{4}$
Maximum area
$A=xy$
$=\frac{p}{4}\times\frac{p}{4}$
$=\frac{p^2}{16}$
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