Question

the right triangle on the right is a scaled copy of the right triangle on the left. identify the scale factor. express your answer as a whole number or fraction in simplest form.

Explanation:

Step1: Recall the formula for scale factor

Scale factor \(=\frac{\text{Length of side in scaled - copy}}{\text{Length of corresponding side in original}}\)

Step2: Identify corresponding sides

Let's take the vertical sides. The vertical side of the original triangle is \(3\), and the vertical side of the scaled - copy is \(\frac{4}{3}\). Or we can take the horizontal sides. The horizontal side of the original triangle is \(4\), and the horizontal side of the scaled - copy is \(1\)
Using the horizontal sides:
Scale factor \(=\frac{1}{4}\times\frac{4}{1}=\frac{1}{4}\) (using \(\text{Scale factor}=\frac{\text{Scaled - copy side}}{\text{Original side}}\), for horizontal sides: \(\frac{1}{4}\), for vertical sides: \(\frac{\frac{4}{3}}{3}=\frac{4}{9}\) (wrong). Using the correct pair:
If we consider the original triangle as the left - hand side triangle (sides \(3\) and \(4\)) and the scaled - copy as the right - hand side triangle (sides \(\frac{4}{3}\) and \(1\)).
We know that \(\text{Scale factor}=\frac{\text{Scaled - copy side}}{\text{Original side}}\). Let's use the horizontal sides: original horizontal side \(x = 4\), scaled - copy horizontal side \(x'=1\)

$$ \text{Scale factor}=\frac{1}{4} $$

Answer:

\(\frac{1}{4}\)