If the two triangles are similar then their angles have the same measure. This also implies that the quotient between a side of one triangle and its corresponding side in the other one is the same for the three pairs of sides. The sides of the large triangle are 9, 2+y and 12 and their corresponding sides in the small triangle are 3, 2 and x. Then since the quotient between corresponding sides is always the same we get:
[tex]\begin{gathered} \frac{9}{3}=\frac{2+y}{2}=\frac{12}{x} \\ 3=\frac{2+y}{2}=\frac{12}{x} \end{gathered}[/tex]
So for x we get:
[tex]3=\frac{12}{x}[/tex]
We multiply both sides by x and we get:
[tex]\begin{gathered} 3\cdot x=\frac{12}{x}\cdot x \\ \\ 3x=12 \end{gathered}[/tex]
And we divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]
Then for y we get:
[tex]3=\frac{2+y}{2}[/tex]
We can multiply both sides by 2:
[tex]\begin{gathered} 3\cdot2=\frac{2+y}{2}\cdot2 \\ 6=2+y \end{gathered}[/tex]
And we substract 2 from both sides:
[tex]\begin{gathered} 6-2=2+y-2 \\ y=4 \end{gathered}[/tex]
So x=4 and y=4. Then the answer to part 1 is option A and the answer to part 2 is option B.
