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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?

 Jun 13, 2021
 #1
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The greatest possible perimeter is 33.

 Jun 13, 2021
 #3
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Is this incorrect?  The other guy gave the same answer.  Why the negatives?  

Guest Jun 13, 2021
 #5
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I have not looked at any of the answers but most likely the negatives are because there is an answer with no explanation.

This is never encouraged but there is at least one troll on here that gets great pleasure from putting up answers like this that are wrong.

You should never pay much attention to unsupported answers.

Melody  Jun 14, 2021
 #2
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The sides are 4, 12, and 17 for a perimeter equal 33.  

 Jun 13, 2021
 #4
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In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 17. What is the greatest possible perimeter of the triangle?  

 

There's probably some formula that could be set up, but I'm not that good.  I have to try brute force. 

 

All I know is, is that the sum of the lengths of two sides of a triangle must exceed the length of the third side. 

 

33, as above, is good if we assume that 17 is the longest side.  But what if it's not? 

 

Here are some other triangles.  I'll list 17 first in each case, since that side remains constant:

 

17, 5, 15   okay  

17, 6, 18   okay  

17, 7, 21   okay  

17, 8, 24   okay  

17, 9, 27   NOPE that won't work because 9 + 17 is not greater than 27.  

 

So my conclusion is that the greatest possible perimeter is 49 units, in the 17, 8, 24 triangle.  

.

 Jun 13, 2021

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