+0  
 
+1
181
3
avatar+28 

What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?

 Jul 17, 2020
 #1
avatar+783 
+1

This is probably wrong but i'll give it a try.

 

The two smallest integers we have are 1 and 2...the sum of the sides would be smallest if the triangle is a right triangle, because it minimizes the third side. Then we can apply the pythagorean theorem to this:

 

1^2+2^2=c^2

1+4=c^2

c^2=5

c=\(\sqrt{5}\).

 

Then the sides of this triangle are 1, 2, and \(\sqrt{5}\). Adding them together we have 1+2+\(\sqrt{5}\)=(3+\(\sqrt{5}\)) units.

 Jul 17, 2020
edited by gwenspooner85  Jul 17, 2020
 #2
avatar
+1

assuming this is positive, your answer would be 9

This is because 2-3-4 is consecutive and follows the triangle inequality theorem

 Jul 17, 2020
 #3
avatar+19 
+1

3 + 4 + 5 = 12 could work. It's probably not the smallest.

 Jul 17, 2020

29 Online Users

avatar
avatar