Question 90
A triangle has side lengths $a$, $b$, $c$ and perimeter $3$. Prove that
a) it is not possible that all the altitudes have integer length;
b) if $\sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} = 3$, then the triangle is equilateral.
a) it is not possible that all the altitudes have integer length;
b) if $\sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} = 3$, then the triangle is equilateral.