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If h, h', h'' denote the lengths of the three altitudes of a triangle, which of the following ratios never occurs as the ratio h: h': h''?

a)2 : 3 : 4

b)2 : 3 : 5

c)2 : 4 : 5

d)3 : 4 : 5

e)3 : 4 : 6

Any help would be much appreciated!
If possible, please could you explain the solution.

Thanks in Advance

Suppose that there is a triangle with altitudes $h_1$, $h_2$ and $h_3$.

Let $a_1$, $a_2$, and $a_3$ be the three sides of this triangle, such that the altitude from side $a_i$ is $h_i$. The area $A$ of the triangle is, by the well known formula:
$$
A=frac{1}{2}a_1h_1=frac{1}{2}a_2h_2=frac{1}{2}a_3h_3.
$$
With this, we use the condition that for a triangle to exist, the sum of the length of its shorter sides must be bigger than the length of its longer side. In terms of altitudes, if $h_1leq h_2leq h_3$, the condition thus becomes
$$
frac{1}{h_1} leq frac{1}{h_2}+frac{1}{h_3},
$$
which does not hold for b) only.

Sum of two altitudes is greater than the third altitude which is not satisfied by option (b).
As if we take them to be 2x,3x and 5x
2x+3x=5x(and it doesn't satisfy).
Cheers!