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.
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