As shown in the diagram, BC is the perpendicular bisector of AD. Solve for BD. Show your work.

Answer:
52 units
Step-by-step explanation:
We can set 7x+10 equal to 9x-2, as BC bisects AD.
7x+10=9x-2 - Now we can isolate the variable
-2x=-12
x=6
Now, all we need to do is plug in 6 into one of our expressions:
7(6)+10=52