Prove that there is no triangle whose altitudes are of length 4, 7, and 10 units.

Let

**a,b,c** represent the lengths of the triangle sides in non-increasing order and

**S **its area.

**2*S=4a=7b=10c**

**a** should be less than **b+c .**

**S/4 **should be less than **S/7+S/10.**

But** 1/4=.25 17/70=.2467**

**So - no such triangle**