In parallelogram ABCD, the diagonals intersect at point O, the perimeter of ABO is 21 cm.

In parallelogram ABCD, the diagonals intersect at point O, the perimeter of ABO is 21 cm. The diagonals AC and BD are 15 cm and 11 cm, respectively. Find side AB.

At point O, the diagonals of the parallelogram are halved, and the halves of the diagonals are the sides of the triangle AO and BO. Therefore, the sides AO and ВO are equal, respectively

15: 2 = 7.5 cm AO side length

11: 2 = 5.5 cm side length ВО

Now we know the perimeter of the triangle and its two sides. To find the unknown side, we need to subtract the sum of its two known sides from the perimeter:

21 – (7.5 + 5.5) = 21 – 13 = 8 cm length of side AB.

Answer: the length of the AB side is 8 cm.