Finding a Side

The scale factor is not always a whole number, and the unknown can be on either triangle. A proportion handles every case: matching sides have the same ratio.

$\frac{DE}{AB} = \frac{FD}{CA}$

Here AB = 4, DE = 10 and CA = 6, so $\frac{10}{4} = \frac{x}{6}$. Multiply both sides by 6: $x = \frac{60}{4} = 15$. The factor was 2.5. If the unknown were on the small triangle instead, the same proportion would work with the letter on the other side.