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

December 27, 2020 | education

| **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.

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