Geometry: Buildings in the triangle Other triangles with the same property:
$1.$ 12 18 6 12 30 102
$2.$ 15 30 15 15 15 90
$3.$ 24 30 54 24 6 42
$4.$ 30 10 40 30 20 50 (proposed problem in sense of clockwise)
$5.$ 36 12 6 12 18 96
$6.$ 36 18 6 36 6 78
$7.$ 42 6 36 42 12 42
$8.$ 60 6 57 30 3 24
$9.$ 60 24 12 12 6 66
Using matlab we can find all triangles (integer solutions) with this property sums of squares: