Question

In a $\Delta$ $ABC$, $D,E,F$ are respectively, the mid- points of $BC,CA,andAB$. If the lengths of side $AB$, $BC$ and $CA$ are $7cm$, $8cm$, $9cm$, respectively, find the perimeter of $\Delta$ DEF.

• A. $12cm$
• B. $21cm$
• C. $24cm$
• D. $16cm$

Answer 1

Answer: (A)

$12cm$

Since, $D,E,F$ are the midpoints of $BC$,$CA$ and $AB$,Thus
$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=2$
$△ABC\sim △DEF$
Now,
Perimeter of $△DEF=DE+EF+DF$
$=\frac{AB}{2}+\frac{BC}{2}+\frac{AC}{2}$
$=\frac{7}{2}+\frac{8}{2}+\frac{9}{2}$
$=\frac{7+8+9}{2}$
$=\frac{24}{2}$
$=12$ cm.