Problem:
Triangle ABC has AB=13 and AC=15, and the altitude to BC has length 12. What is the sum of the two possible values of BC ?
Answer Choices:
A. 15
B. 16
C. 17
D. 18
E. 19 Solution:
Let D be the foot of the altitude to BC. Then BD=132−122​=5 and DC=152−122​=9. Thus BC=BD+DC=5+9=14 or BC=DC−BD=9−5=4. The sum of the two possible values is 14+4=18​.
