... I tackled it with a thick pencil, graph paper, and without Pythagoras!
Your measurements might just fit if you place a long side of the house on the northwest side (with a 3-meter border distance). But only if the building boundary limits the garden side to a maximum of 10 meters of garden. If the garden needs to be 12 meters deep, then the measurements no longer fit (unfortunately estimated... 10 meters would be understandable). Then you would already touch the 3-meter border in the south with your house but at least have a big garden feeling with a southeast orientation.
If you place the house parallel to the south side, you would only have a 4-meter garden strip to the south.
With a 10 x 10 meter house you would only have a 3-meter strip in the south as well :-(
Personally, I could come to terms with or get used to the first alternative, since the sun also appears in the north in summer, for example, and in winter it sets anyway at 7 o’clock. A utility room in the north tip of the house would mean a long connection line (about 15 meters) for the hookups. At least 12.5 are included in the price of the providers here. Regarding the terrace, I always say: it tends toward the 2nd or 3rd terrace :)... you don’t need a terrace for sunbathing, but rather a secluded area in the garden where the sun reaches.
That’s from me, but really only with an unsharpened pencil. If I were you, I would take the time to calculate everything precisely. It’s possible with Pythagoras, calculate the rear building boundary from the proportions.
Have fun :D