MATHCOUNTS Exercises – 12

In $\triangle{ABC}$, $\overline{AB}=5$, $\overline{AC}=6$, $\overline{BC}=7$. Square $BCED$ is drawn along the side of $\overline{BC}$, as shown in the following figure. Find the area of $\triangle{ADE}$. Click here for the hint.

Hint Draw the altitude from $A$ of $\triangle{ABC}$ intersecting $\overline{BC}$ at $F$ and $\overline{DE}$ at $G$. Try to find the length of $\overline{AF}$ and $\overline{AG}$.