Çözüldü Coordinate Geometry - Natural Numbers (8th Grade)

For a rectangle with one vertex at the origin and sides lying along the coordinate axes of the Cartesian plane, if another vertex of this rectangle lies on the diagonal defined by -x / 5 + y / 3 = 0 and the coordinates of this vertex are integers, what is the minimum possible perimeter, in the selected units, of the rectangle?

The ordinate of the vertex on the diagonal is y = 3x / 5,
Perimeter of the rectangle: P(x) = 2(x + 3x / 5) = 16x / 5
Minimum perimeter in units: P(5) = 16 units.

Original Question (Turkish): "8. Sınıf Matematik Soru Bankası", Hız Yayınları, Nisan 2025, Sayfa 194, Test 91, (Çizimli) Soru 7