The base of a trapezoid is $a$, the parallel side is $b$, and its height is $m$. What is the height of the triangle formed by extending the non-parallel sides?
A trapez non-parallel sides, when extended, form two similar triangles. If we denote the height we are looking for by \( x \), then

\[
a: b = m + x: x, \text{ or } a - b: b = m: x
\]

from which

\[
x = m \frac{b}{a - b}
\]

Freund Ernö

Number of solutions: 18.