Question

if triangle abc is similar to triangle def and the length of ab is 5 units while the length of de is 10 units, what is the scale factor from triangle abc to triangle def?
a. 2
b. 10
c. 5
d. $\frac{1}{5}$

Explanation:

Step1: Recall scale factor formula

The scale factor from triangle \(ABC\) to triangle \(DEF\) is the ratio of the length of a side in \(DEF\) to the corresponding side in \(ABC\). So, if \(AB\) (in \(ABC\)) corresponds to \(DE\) (in \(DEF\)), the scale factor \(k=\frac{DE}{AB}\).

Step2: Substitute the given values

We know \(AB = 5\) units and \(DE=10\) units. Substituting these values into the formula, we get \(k=\frac{10}{5}\).

Step3: Simplify the fraction

Simplifying \(\frac{10}{5}\) gives \(2\).

Answer:

a. 2