Chapter: Pythagoras Theorem· Mathematics Part 2 (Geometry)
Answer: \(2\sqrt{14}\) cm (about 7.48 cm)
In a parallelogram, the sum of the squares of the four sides equals the sum of the squares of the diagonals (this follows from Apollonius theorem, since the diagonals bisect each other).
\(6^2 + 8^2 + 6^2 + 8^2 = 12^2 + d^2\) \(\therefore 200 = 144 + d^2\) \(\therefore d^2 = 56\) \(\therefore d = \sqrt{56} = 2\sqrt{14}\) cm.