SOLUTION: What is the smallest possible integer perimeter of a triangle which has sides 5 and 10?

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Question 815953: What is the smallest possible integer perimeter of a triangle which has sides 5 and 10?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The third side must be larger than 10-5 = 5 units.

Let x be the third unknown side. So if the third side must be larger than 5 units, then we can say x > 5.

The perimeter of the triangle is

P = s1 + s2 + s3

P = 5+10+x

P = 15+x

Now if x > 5, then this means that 15+x > 20 (add 15 to both sides of the original inequality)

So the perimeter must be larger than 20 units. If the perimeter is an integer (or whole number), then the smallest it can be is 21 units.