A rectangular sign that has dimensions $9 \mathrm{~m}$ by $16 \mathrm{~m}$ has a square advertisement painted on it. The border around the square is required to be at least $1.5 \mathrm{~m}$ wide. The area of the largest square advertisement that can be painted on the sign is
(A) $78 \mathrm{~m}^{2}$
(B) $144 \mathrm{~m}^{2}$
(C) $36 \mathrm{~m}^{2}$
(D) $9 \mathrm{~m}^{2}$
(E) $56.25 \mathrm{~m}^{2}$
A rectangular sign that has dimensions $9 \mathrm{~m}$ by $16 \mathrm{~m}$ has a square advertisement painted on it. The border around the square is required to be at least $1.5 \mathrm{~m}$ wide. The area of the largest square advertisement that can be painted on the sign is
(A) $78 \mathrm{~m}^{2}$
(B) $144 \mathrm{~m}^{2}$
(C) $36 \mathrm{~m}^{2}$
(D) $9 \mathrm{~m}^{2}$
(E) $56.25 \mathrm{~m}^{2}$

## Solution

If the $9 \times 16$ rectangle has a square painted on it such that the square must have a border of width $1.5 \mathrm{~m}$ this means that the square has a maximum width of $9-1.5-1.5=6$. So the largest square has an area of $6 \mathrm{~m} \times 6 \mathrm{~m}$ or $36 \mathrm{~m}^{2}$.

ANswer: (C)