Final answer:
In parallelogram ABCD where AB = 9cm, BC = 13cm, and AC = 20cm, the length of BD is approximately 15.81 cm.
Step-by-step explanation:
In parallelogram ABCD, the opposite sides are equal in length. So, AB = CD and BC = AD. Given AB = 9cm and BC = 13cm. To find the length of BD, we can use the Pythagorean Theorem.
Using the Pythagorean Theorem, we have:
AB^2 + BC^2 = BD^2
9^2 + 13^2 = BD^2
81 + 169 = BD^2
250 = BD^2
BD = √250
BD ≈ 15.81 cm