The diagonals of a rhombus are 6 and 10, find the sides and corners of a quadrilateral

The diagonals of a rhombus are 6 and 10, find the sides and corners of a quadrilateral with vertices at the midpoints of the sides of this rhombus.

Let the points K, H, P and M be the midpoints of the sides of the rhombus, then in the triangle ABC the segment KН is its midline, then KН = AC / 2 = 10/2 = 5 cm.

Similarly, МР = АС / 2 = 10/2 = 5 cm, КМ = НР = ВD / 2 = 6/2 = 3 cm.

The diagonals of the rhombus at point O intersect at right angles. KН is parallel to AC, KM is parallel to ВD, VD is perpendicular to AC, then KM is perpendicular to KН, and then the quadrangle of KНРM is a rectangle.

Answer: The sides of the КНРM quadrangle are 5 cm and 3 cm, the angles of the quadrilateral are 90.