# What is the maximum? What are the principles?

Jun 20, 2018

$\text{B. 9}$

#### Explanation:

If a\ &\ b are known altitudes of a triangle where $a < b$ then the third altitude ($c$) should satisfy the relation

$\frac{a b}{a + b} < c < \frac{a b}{b - a} \textcolor{w h i t e}{\ldots}$[Click here for derivation]

(6 × 14)/(6 + 14) < c < (6 × 14)/(14 - 6)

$\frac{84}{20} < c < \frac{84}{8}$

$4.2 < c < 10.5$

From the choices given $\text{B. 9}$ is the correct option.