A3. Three squares are placed in a row such that each subsequent one has a side that is $1 \mathrm{~cm}$ longer. All three together have an area of $302 \mathrm{~cm}^{2}$. How many centimeters long is the side of the largest square?
(A) 9
(B) 10
(C) 11
(D) 12
(E) None of the above.
A3. The area of the smallest square is $a^{2}$, the area of the second is $(a+1)^{2}$, and the area of the largest is $(a+2)^{2}$. Therefore, $a^{2}+(a+1)^{2}+(a+2)^{2}=302$. We rearrange this equation to $a^{2}+2 a-99=0$ and factorize: $(a-9)(a+11)=0$. The meaningful solution is $a=9 \mathrm{~cm}$. The side of the largest square is $11 \mathrm{~cm}$ long.

We have a bit less calculation if we choose the side lengths of the squares in sequence as $a-1, a$, and $a+1$. Then we have $a^{2}-2 a+1+a^{2}+a^{2}+2 a+1=302$, from which we get $3 a^{2}=300$ and $a=10$. The side of the largest square is $11 \mathrm{~cm}$ long.