In a school, auditorium was used for its cultural activities. The shape of the floor of the auditorium is rectangular with dimensions x and y (x > y), has fixed parameter p.

Based on the above information answer the following questions.

The value of y, for which area of floor of auditorium is maximum is :

$\frac{p}{4}$

p = 2x + 2y

at $x = \frac{p}{4}$ → area maximum

so $p = \frac{2p}{4} +2y$

⇒ $p - \frac{p}{2} = 2y$

⇒ $y = \frac{p}{4}$ → for max. area