## Task B-1.4.

On the side $\overline{A B}$ of the rectangle $A B C D$, a point $E$ is chosen, and on the side $\overline{C D}$ a point $F$ such that the quadrilateral $E B F D$ is a rhombus. Determine the length of the segment $\overline{E F}$ if the lengths of the sides of the rectangle are $a=|A B|$ and $b=|B C|,|A B|>|B C|$.
## Second Solution.

Consider the figure given in the first solution. Triangles $D F G$ and $D B C$ are similar by the $\mathrm{K}-\mathrm{K}$ theorem (they share a common angle at vertex $D$ and one right angle).

Then,

$$
\begin{aligned}
\frac{|B D|}{2 a} & =\frac{|E F|}{2 b} \\
|E F| & =\frac{b}{a} \cdot|B D| \\
|E F| & =\frac{b}{a} \cdot \sqrt{a^{2}+b^{2}}
\end{aligned}
$$