Question

Correspondence $ABC⟷DEF$ of $△ABC$ and $△DEF$ is similarity. If $AB+BC=10$ and $DE+EF=12$ and $AC=6$ then $DF$=_____

• A. $6$
• B. $5$
• C. $7.2$
• D. $16$

Answer 1

Answer: (C)

$7.2$

$\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}=K$

$AB+BC=10$

$\Rightarrow K(DE+EF)=10$

$K=\frac{10}{2}$

$AC=KDF$

$\Rightarrow 6=\frac{10}{12}\left(DF\right)$

$\Rightarrow DF=7.2$