Question

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

Explanation:

Step1: Convert mixed numbers to improper fractions

$1\frac{1}{2}=\frac{3}{2}$, $2\frac{2}{5}=\frac{12}{5}$, $4 = \frac{4}{1}$, $6\frac{2}{5}=\frac{32}{5}$

Step2: Calculate the scale factor using side lengths

We can use either pair of corresponding sides. Let's use the side of length $4$ (triangle $U$) and $6\frac{2}{5}$ (triangle $W$).
Scale factor $k=\frac{\text{Length in }W}{\text{Length in }U}$
$k = \frac{\frac{32}{5}}{4}=\frac{32}{5}\times\frac{1}{4}=\frac{8}{5} = 1\frac{3}{5}$
Alternatively, using the top - side: $\frac{\frac{12}{5}}{\frac{3}{2}}=\frac{12}{5}\times\frac{2}{3}=\frac{8}{5}=1\frac{3}{5}$

Answer:

The scale factor is $\frac{8}{5}$ (or $1\frac{3}{5}$)