Question

Can the sides of a triangle have lengths 6.2, 0.5, and 7.8? yes or no

Answer 1

No, it's not possible for the sides of a triangle to have those lengths.

According to the triangle inequality theorem, the sum of any two sides of the triangle has to be bigger than the last side. Let's test this.

$6.2+7.8\ \textgreater \ 0.5$

This inequality satisfies the triangle inequality theorem.

$7.8+0.5\ \textgreater \ 6.2$

This also satisfies the theorem.

$6.2+0.5 \textless \ 7.8$

Uh oh. This does not satisfy the triangle inequality theorem. Thus, it is not possible for a triangle to have these side lengths.