In parallelogram ABCD the sides are AB = 7 cm and BC = 9 cm, and the diagonal AC measures 8 cm. What is the length of the other diagonal BD?

In every parallelogram the sum of the squares of the diagonals equals the sum of the squares of the four sides: $A{C}^2+B{D}^2=2(A{B}^2+B{C}^2)$. So $64+B{D}^2=2(49+81)=260$, giving $B{D}^2=196$ and $BD=14$ cm. Dropping the factor 2 leaves $B{D}^2=130-64=66$ and the trap √66 cm. Choosing 8 cm assumes the diagonals are equal, which happens only in a rectangle.