Question

If the sides of a triangle are 17,25 and 28, then find the greatest length of the altitude.

Answer 1

we know from geometry that the greatest altitude is perpendicular to the
shortest side.
Let $a=17,b=25$ and $c=28$
$\therefore \Delta =\frac{1}{2}AD\times BC$ or
$AD=\frac{2\Delta }{17}$
${\Delta }^2=s(s-a)(s-b)(s-c)={210}^2$ $\Rightarrow AD=\frac{420}{17}$