Answer:
BD = 12 :)
Explanation:
Alright, we'll need the Pythagorean theorem for this!
So, the length of AC is 10. That means the lengths of AD and DC are both half of that, which is 5 :)
DC = 5
We already know that BC = 13, so we can plug in these values into the pythagorean theorem for the right triangle BDC:
BD^2 + DC^2 = BC^2
BD^2 + 5^2 = 13^2
BD^2 + 25 = 169
BD^2 = 169 - 25 = 144
BD = √144 = 12 :)