# If the integer lengths of the three sides of a triangle are 4, x and 9, what is the least possible perimeter?

Jul 21, 2016

Let $a$, $b$ and $c$ be the sides of a scalene triangle, $c$ being the longest in length.

The statement a + b ≥ c must be true, because otherwise the shape formed would not be a triangle since the sides wouldn't be touching at the vertices (it would be an open shape(.

Let $x$ be $b$. Then 4 + b ≥ 9, or the least possible value of $b$ is $5$.

The minimum perimeter of the triangle is therefore $4 + 5 + 9 = 18$.

Hopefully this helps!