The length of BC = 72
Solution:
Given ΔABC and ΔDEF are similar triangles.
ΔABC [tex]\sim[/tex] ΔDEF
AB = 54, BC = n, EF = 12, DE = 9
Similar triangle theorem:
If two triangles are similar then the corresponding sides are proportional to each other.
[tex]$\Rightarrow\frac{BC}{EF}=\frac{AB}{DE}[/tex]
Substitute the given values, we get
[tex]$\Rightarrow\frac{n}{12}=\frac{54}{9}[/tex]
Do cross multiplication.
[tex]$\Rightarrow9\times n=54\times12[/tex]
Divide both sides of the equation by 9.
[tex]$\Rightarrow n=\frac{54\times12}{9}[/tex]
[tex]$\Rightarrow n=6\times12[/tex]
[tex]$\Rightarrow n=72[/tex]
⇒ BC = 72
Option B is the correct answer.
The length of BC = 72.
