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.

Maximum area of floor is :

$\frac{p^2}{4}$ $\frac{p^2}{16}$ $\frac{p^2}{28}$ $\frac{p^2}{64}$

$\frac{p^2}{16}$

Maximum area = xy    $(x = \frac{p}{4},  ~~y = \frac{p}{4})$ = $\frac{p}{4} × \frac{p}{4} = \frac{p^2}{16}$