0
$\begingroup$

In $ \Delta ABC , m\angle CBA = 72 . $ $E$ is the midpoint of $AC$ and $D$ is on $BC$ such that $2BD = DC$.$AD \cap BE = {F}$.
Area of $\Delta BDF = 10 . $ Find area of $\Delta DEF$

$\endgroup$
  • $\begingroup$ What have you attempted? $\endgroup$ – Allawonder Jun 27 '18 at 16:23
0
$\begingroup$

Let $K$ be a midpoint of $DC$.

Thus, since $E$ is a midpoint of $AC$, we obtain that $EK||AD$ and since $D$ is a midpoint of $BK$, we obtain $BF=FE$ and $$S_{\Delta FDE}=S_{\Delta BDF}=10.$$

$\endgroup$
0
$\begingroup$

The areas will be the same; $[\Delta DEF]=10$. We begin my using mass points letting $F$ be the center of mass. If we let $B$ have a mass of 2 so that $C$ has a mass of 1, then $A$ must also have a mass of 1 since $E$ is the midpoint. Then $DF/FA=1/3$ so $[\Delta BFA]=30$. Similarly, $BF/FE=1$ since $B$ and $E$ both have mass $2$. Thus, $[\Delta AFE]=30$ as well. Then using $DF/FA=1/3$ again, $[\Delta DFE]=10$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.