# 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.