SOLUTION: two sides of a triangle have lengths 12 and 15. What are the possible lengths of the third side

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Question 265888: two sides of a triangle have lengths 12 and 15. What are the possible lengths of the third side
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
A%5E2%2BB%5E2=C%5E2
"A" and "B" being the two smaller sides and "C" the longest
what you do know is:
15>12 so 12 cant be "C"
If 12 is "A" and 15 is "C" then "B" is one possible answer
If 12 is "A" and 15 is "B" then "C" is one possible answer
so we make 2 seperate equations
12%5E2%2BB%5E2=15%5E2
12%5E2%2B15%5E2=C%5E2
___________
144%2BB%5E2=225
B%5E2=225-144
sqrt%28B%5E2%29=sqrt%2881%29
B=9
___________
12%5E2%2B15%5E2=C%5E2
144%2B225=C%5E2
sqrt%28369%29=sqrt%28C%5E2%29
sqrt%28369%29=C%29
___________
answer: 9 or sqrt%28369%29