# O the point of intersection of the parallelogram diagonals ABCD, E and F are the midpoints of sides AB

**O the point of intersection of the parallelogram diagonals ABCD, E and F are the midpoints of sides AB and BC, OE = 4 cm, OF = 5 cm.Find the perimeter of ABCD**

Let us prove that the segments OE and OF are equal to half the lengths of the sides AB and BC, respectively.

In triangle ABC, point O is the middle of BD, as the middle of the intersection of the diagonals, which are halved at the point of intersection. IN = DO. Point E is the middle of side AB by condition Then OE is the middle line of triangle ABC and is equal to half of side AD.

Then AD = OE * 2 = 4 * 2 = 8 cm.

Similarly, in the BCD triangle, the segment OF is the middle line of the triangle, then DS = OF * 2 = 5 * 2 = 10 cm.

In a parallelogram, the opposite sides are equal, then BC = AD = 8 cm, AB = CD = 10 cm.

Determine the perimeter of the parallelogram.

P = AB + BC + CD + AD = 10 + 8 + 10 + 8 = 36 cm.

Answer: The perimeter is 36 cm.