Question 28
On a line $r$ the points $A$ and $B$ are marked, and on a line $s$, parallel to $r$, the points $C$ and $D$ are marked, in such a way that $A B C D$ is a square. The point $E$ is also marked on the segment $C D$.
a) What is the ratio between the areas of the triangles $A B E$ and $B C D$ if $E$ is the midpoint of $C D$?
b) What must the ratio $\frac{D E}{E C}$ be so that the area of the triangle $B F E$ is twice the area of $D F E$, where $F$ is the intersection of the segments $A E$ and $B D$?
a) What is the ratio between the areas of the triangles $A B E$ and $B C D$ if $E$ is the midpoint of $C D$?
b) What must the ratio $\frac{D E}{E C}$ be so that the area of the triangle $B F E$ is twice the area of $D F E$, where $F$ is the intersection of the segments $A E$ and $B D$?