Question

Correspondence ABC $\leftrightarrow$ 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

The correct option is C $7.2$

$△ABC$ and $△DEF$ are similar.

Then their corresponding sides are proportional.

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

Also, $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{AB+BC+AC}{DE+EF+DF}$

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

$\frac{6}{DF}=\frac{10+6}{12+DF}$

$5DF=36$

$DF=7.2cm$