The sum of the two diagonals of a quadrilateral is 9.8 cm. Find the perimeter of the quadrilateral whose vertices

The sum of the two diagonals of a quadrilateral is 9.8 cm. Find the perimeter of the quadrilateral whose vertices are the midpoints of the sides of this quadrilateral.

Let the length of the diagonal AC = X cm, and the length of the diagonal VD = Y cm.
Then X + Y = 9.8 cm.
In the triangle ABC, the segment KM is its middle line, since points K and M are the middle of the sides AB and BC, then KM = AC / 2 = X / 2 cm.
Similarly, HP = X / 2 cm.
In the AED triangle, the KR segment is the middle line, then KR = ВD / 2 = Y / 2.
Similarly, MH = Y / 2 cm.
Rkmnr = KM + MN + NR + KR = X / 2 + Y / 2 + X / 2 + Y / 2 = X + Y = 9.8 cm.
Answer: The perimeter of the quadrangle is 9.8 cm.