Question

are the triangles similar? if so what is the scale factor?

Answer 1

a) Yes, The scale factor is 3/2

Explanation

Step 1

to check if the triangles are similar, we need to prove that the ratios of the longest side and one sideof the triangle are similar

so

let

$ratio=\frac{longest\text{ side}}{side}$

hence

$\begin{gathered} ratio_1=\frac{8}{5}=1.6 \\ ratio_2=\frac{12}{7.5}=1.6 \end{gathered}$

therefore, the triangles are similar

Step 2

now, to find the scale factor we use the formula

$scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}}$

so, let's take the longest side on each triangle

$\begin{gathered} final\text{ length=12} \\ original\text{ length=8} \end{gathered}$

replace and calculate

$\begin{gathered} scale\text{ factor =}\frac{final\text{ length }}{original\text{ length}} \\ scale\text{ factor =}\frac{12}{8}=\frac{3}{2} \end{gathered}$

therefore, the answer is

a) Yes, The scale factor is 3/2

I hope this helps you