In parallelogram ABCD, the diagonals are 2 cm and 6 cm. Calculate the side BC if AB = √11 cm.

According to one of the signs of a parallelogram, the sum of the squares of its diagonals is equal to the sum of the squares of its sides, i.e.:

AC ^ 2 + BD ^ 2 = AB2 ^ + BC ^ 2 + CD ^ 2 + AD ^ 2.

Knowing also that the opposite sides of the parallelogram are equal (AB = CD), we write this equality with all known values:

6 ^ 2 + 2 ^ 2 = 2 * (sqrt11) ^ 2 + 2 * BC;

36 + 4 = 22 + 2 * BC;

40 = 22 + 2 * BC;

2 * BC = 18;

BC = 9cm.

Answer: BC = 9cm.