Question 1164158: A triangle has two sides of length 15 and 3. What is the largest possible whole-number length for the third side?
Found 3 solutions by ikleyn, Edwin McCravy, Theo:
Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website! .
According to triangle inequalities, the third side should be shorter than the sum of the lengths
of the two other sides 15 + 3 = 18.
At the same time, the third side must be longer than the difference of the two other sides 15-3 = 12.
So, under the given conditions, the third side should be integer from 12 to 18 exclusive, i.e. one of the values 13, 14, 15, 16, 17.
The largest possible whole-number length for the third side is 17. ANSWER
Solved, answered and explained.
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
For every triangle whose sides are a, b, and c, these three inequalities
must hold:
a+b < c
a+c < b
b+c < a
So every triangle whose sides are 15, 3, and c, these three inequalities
must hold:
15+3 > c
15+c > 3
3+c > 15
These become
18 > c
c > -12 <--that will always hold!
c > 12
So 12 < c < 18
So the only values for the third side are between 12 and 18, exclusive.
That means the third side is either 13, 14, 15, 16 or 17.
The largest possible whole number length is 17.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the sum of the length of two sides of a triangle must be greater than the length of the third side.
the sum of 15 and 3 is 18 which must be greater than the length of the third side.
the length of the third side must be less than 18.
the next integer below 18 is 17.
that should be your solution.
the largest possible whole number length for the third side is 17.
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