Answer:
z = 8 in
Explanation:
The greater and smaller triangle are similar, so the ratio of the corresponding sides is constant. Then, we can write the following equation:
[tex]\frac{3}{3+3}=\frac{4}{z}[/tex]
Solving for z, we get:
[tex]\begin{gathered} \frac{3}{6}=\frac{4}{z} \\ 3\cdot z=6\cdot4 \\ 3z=24 \\ \frac{3z}{3}=\frac{24}{3} \\ z=8 \end{gathered}[/tex]
Therefore, the value of z is 8 in.
