Question

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

Answer 1

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!