BC = 13
AC = 10
BD = x
We want to find what x is. You know what we can do? We can use the PYTHAGOREAN THEOREM. The PT states:
[tex] a^{2} + b^{2} = c^{2} [/tex]
But we need to know DC in order to use the PT. But in Geometry there’s this theorem (I forgot sorry!) that states that BD divides ABD and CBD. Thus DC = 5 (half).
Pythagorean Theorem:
[tex] 13^{2} - 5^{2} = BD^{2} [/tex]
169 - 25 = 144
[tex] \sqrt{144} [/tex] = 12
BD = 12.
Hope this helps!
