Points B and C lie on AD as shown below. The length of AD is 30 units

Points B and C lie on AD as shown below. The length of AD is 30 units; AC is 16 units long; and BD is 20 units long. How many units long, if it can be determined, is BC?

1. 4
2. 6
3. 10
4. 14
5. Cannot be determined from the given information 

Answer

The correct option is B.

BC is the intersection of AC and BD. So, the sum of the lengths of AC and BD would be the same as the sum of the lengths of AD and BC.

AC = AB + BC, BD = BC + CD, and AD = AB + BC + CD

AC + BD = AB + BC + BC + CD = AB + BC + CD + BC = AD + BC

AD + BC = AC + BD

30 + BC = 16 + 20

30 + BC = 36

BC = 6