# Triangle inequality

Geometry Level 4

Find the smallest number $$N$$ for which the following inequality holds in every triangle.

$${ h }_{ a }{ h }_{ b }{ h }_{ c }\le N\cdot abc$$

Approximate the value to two decimal places.

$${ h }_{ a }$$ is the height that falls on the side a. The same is with $${ h }_{ b }$$ and $${ h }_{ c }$$

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