# The diagonals of the parallelogram ABCD intersect at point O. The diagonal BD is half the diagonal AC

The diagonals of the parallelogram ABCD intersect at point O. The diagonal BD is half the diagonal AC, AO = 4.5 cm. Find: a) AC and BD b) Paob, if AB = 5 cm

The diagonals of the parallelogram intersect at point o and are halved by this point.

a) since the AO segment is 4.5 cm, the AC diagonal will be equal to:

AC = AO · 2;

AC = 4.5 2 = 9 cm.

Since the length of the ВD diagonal is half the length of the AC diagonal, its length will be equal to the length of the AO segment:

ВD = AO = 4.5 cm.

b) The perimeter of triangle AOB is the sum of the lengths of its sides:

P (aov) = AO + OB + AB.

Since the length of the ВD diagonal is 4.5 cm, the length of the AO segment will be equal to half of its length:

ВO = ВD / 2;

BO = 4.5 / 2 = 2.25 cm.

P (aov) = 2.25 + 4.5 + 5 = 11.75 cm.

Answer: a) AC = 9 cm, ВD = 4.5 cm; b) P (aov) = 11.75 cm.

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