The perimeter of a triangle is an integer. If one side of the triangle is $1$, then what is the smallest possible value of the perimeter? (Assume that the triangle is non-degenerate.)

siIviajendeukie Jun 5, 2024

#1**+1 **

The smallest possible perimeter is 3.

Let's say that b is 1.

We would have

\(a < 1 \\ c > 1\)

where

\( a + c = 2 \\ a > .50 \\ c < 1.5 \)

An example would be

\(a = .75\\ b = 1\\ c =1.25\)

Thanks! :)

NotThatSmart Jun 5, 2024

#1**+1 **

Best Answer

The smallest possible perimeter is 3.

Let's say that b is 1.

We would have

\(a < 1 \\ c > 1\)

where

\( a + c = 2 \\ a > .50 \\ c < 1.5 \)

An example would be

\(a = .75\\ b = 1\\ c =1.25\)

Thanks! :)

NotThatSmart Jun 5, 2024