Question

If m - n, m, m + n are the lengths of the sides of an obtuse angled triangle, then find minimum and maximum value of n.

Answer 1

$\Delta$ is obtused
greatest side will be$m+n$.
Smallest side will be $m-n$,
We know that , sum of two sides of a $\Delta$ is greater than 3rd side.
$\therefore$ $m+m-n>m+n$.
$2m-n>m+n.$
$2m-m>n+n$.
$m>2n$
or $2n<m$
$n<\frac{m}{2}$