Question

If two similar triangles have a scale factor of $a:b$, then the ratio of their perimeters is ....

• A. $a^2:b^2$
• B. $a:b$
• C. $a^3:b^3$
• D. None of these

Answer 1

The correct option is B $a:b$

Scale factors of triangle $=a:b$

Let the triangles be $△ABC$ and $△DEF$

Given $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{a}{b}$

$\Rightarrow AB=\frac{a}{b}DE,BC=\frac{a}{b}EF,AC=\frac{a}{b}DF$

$\frac{Perimeter\left(△ABC\right)}{Perimeter\left(△DEF\right)}=\frac{AB+BC+AC}{DE+EF+DF}\Rightarrow \frac{Perimeter\left(△ABC\right)}{Perimeter\left(△DEF\right)}=\frac{\frac{a}{b}DE+\frac{a}{b}EF+\frac{a}{b}DF}{DE+EF+DF}\Rightarrow \frac{Perimeter\left(△ABC\right)}{Perimeter\left(△DEF\right)}=\frac{a}{b}\left(\frac{DE+EF+DF}{DE+EF+DF}\right)=\frac{a}{b}$

So option $B$ is correct.