Question

what is the scale factor from δabc to δuvw?
(image of two right triangles: δabc with legs 3, 4 and hypotenuse 5; δuvw with legs 15, 20 and hypotenuse 25. multiple choice options: a. 20, b. \\(\frac{1}{20}\\), c. 5, d. \\(\frac{1}{5}\\))

Explanation:

Step1: Identify Corresponding Sides

In similar triangles, corresponding sides are proportional. For $\triangle ABC$ and $\triangle UVW$, let's find corresponding sides. Let's take side $AC = 3$ (in $\triangle ABC$) and $UW = 15$ (in $\triangle UVW$), or $BC = 4$ and $VW = 20$, or $AB = 5$ and $UV = 25$.

Step2: Calculate Scale Factor

Scale factor from $\triangle ABC$ to $\triangle UVW$ is $\frac{\text{Length in } \triangle UVW}{\text{Length in } \triangle ABC}$. Let's use $AC = 3$ and $UW = 15$. So scale factor $= \frac{15}{3} = 5$. We can check with other sides: $\frac{20}{4} = 5$ and $\frac{25}{5} = 5$. All give the same scale factor.

Answer:

C. 5