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

awnrs Jul 17, 2020

#1**+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.

gwenspooner85 Jul 17, 2020