Question 89
Filippo's living room has a rectangular floor plan. Filippo noticed that if he plugs the vacuum cleaner into the socket near the front door, he can clean the whole floor: this means that all points of the floor are at distance less than $5~\mathrm{m}$ from the point of the wall where the socket is. What is the maximum possible area of the living room (in $\mathrm{m}^{2}$)?