Question

triangle v is a scaled copy of triangle u. what scale factor takes triangle u to triangle v?

Explanation:

Step1: Convert mixed numbers to improper fractions

$10\frac{4}{5}=\frac{10\times5 + 4}{5}=\frac{54}{5}$, $15\frac{3}{5}=\frac{15\times5+3}{5}=\frac{78}{5}$

Step2: Calculate the scale factor

The scale factor $k$ is the ratio of the corresponding sides of the scaled - copy (triangle $V$) to the original (triangle $U$). Let's use the horizontal sides: $k=\frac{10\frac{4}{5}}{18}=\frac{\frac{54}{5}}{18}$.
Using the rule of dividing by a number is the same as multiplying by its reciprocal: $\frac{\frac{54}{5}}{18}=\frac{54}{5}\times\frac{1}{18}=\frac{54}{90}=\frac{3}{5}$.
We can check with the vertical sides: $\frac{15\frac{3}{5}}{26}=\frac{\frac{78}{5}}{26}=\frac{78}{5}\times\frac{1}{26}=\frac{78}{130}=\frac{3}{5}$

Answer:

$\frac{3}{5}$