The extensions of the lateral sides $A B$ and $C D$ of trapezoid $A B C D$ intersect at point $E$. Find the sides of triangle $A E D$, if $A B=3, B C=10, C D=4, A D=12$.
Consider similar triangles

## Solution

Triangle $E B C$ is similar to triangle $E A D$ with a ratio of $B C / A D = 5 / 6$. Therefore, $B E = 5 A B = 15$, $C E = 5 C D = 20$.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-18.jpg?height=375&width=602&top_left_y=1728&top_left_x=728)

## Answer

$15 ; 20$.