Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be
[tex]\begin{gathered} AB=x \\ BC=y \end{gathered}[/tex]
Then,
[tex]\Rightarrow\frac{x}{5}=\frac{y}{12}=\frac{26}{3}[/tex]
Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.
However, we can algebraically find x and y, although it would not make any sense geometrically speaking.
[tex]\Rightarrow\frac{x}{5}=\frac{26}{3}[/tex]
Solving for x,
[tex]\begin{gathered} \Rightarrow x=\frac{26\cdot5}{3}=43.333\ldots \\ \Rightarrow AB=43.333\ldots \end{gathered}[/tex]
Similarly, solving for y,
[tex]\begin{gathered} \Rightarrow\frac{y}{12}=\frac{26}{3} \\ \Rightarrow y=26\cdot\frac{12}{3}=104 \\ \Rightarrow BC=104 \end{gathered}[/tex]
