Question

the two triangles are similar (dilated). find the scale factor and missing side length. scale factor: ? = ____

Explanation:

Step1: Find the scale - factor

The scale factor is the ratio of corresponding sides. Let's take the ratio of the known corresponding sides. The side of length 3 in the small triangle corresponds to the side of length 9 in the large triangle. The scale factor $k$ is given by $k=\frac{9}{3}=3$.

Step2: Find the missing side - length

The missing side corresponds to the side of length 4 in the small triangle. Since the scale factor $k = 3$, the length of the missing side $x$ is $x=4\times k$. Substituting $k = 3$, we get $x = 4\times3=12$.

Answer:

Scale factor: 3
? = 12