The given scale factor is 3:1.
Recall that the scale factor is equal to the ratio of the lengths of the corresponding sides.
Hence, it follows from the figures that:
[tex]\frac{12}{a}=\frac{9}{b}=\frac{3}{1}[/tex]
Solve each pair of equations to find the value of a and b:
[tex]\begin{gathered} \frac{12}{a}=\frac{3}{1} \\ Cross\text{ multiply:} \\ \Rightarrow3a=12 \\ \text{ Divide both sides by }3: \\ \Rightarrow\frac{3a}{3}=\frac{12}{3} \\ \Rightarrow a=4 \end{gathered}[/tex]
Hence, side a is 4 inches long.
[tex]\begin{gathered} \frac{9}{b}=\frac{3}{1} \\ \text{ Cross multiply:} \\ \Rightarrow3b=9 \\ \text{ Divide both sides by }3: \\ \Rightarrow\frac{3b}{3}=\frac{9}{3} \\ \Rightarrow b=3 \end{gathered}[/tex]
Hence, side b is 3 inches long.
The correct option is A.
