Hey how can I solve this problem? It's from an app called Euclidea, its sooo much fun if you like maths like me ;)?

I'm really enjoying the Euclidea app. I can't find a lot of info on it though. Is there a users' forum anywhere? I don't see how some of these problems are solved in the number of moves they set. It's a really fun "game."

Draw the two diagonals. Construct a line parallel to a and b through the point where the diagonals intersect. The segment of that line from the intersection point to either side of the trapezoid has the length you seek.

move the beginning of a to be on top of beginning of b...

then the line through the ends of a and b has slope - a / b and

equation y - 0 = [ -a/b] (x-b)..now let x = 2ab / [ a +b ] to find the y value where the line belongs