If the altitude of a triangle are in arithmetic progression, then the sides of the triangles are in
If the altitude of a triangle are in arithmetic progression, then the sides of the triangles are in
$\mathrm{AP}$
$\mathrm{HP}$
$\mathrm{GP}$
$\mathrm{AGP}$
Solution
In $\triangle A B C$
$
\Delta=\frac{1}{2} a p_1=\frac{1}{2} b p_2=\frac{1}{2} c p_3
$
where $a, b, c$ length of the sides of the triangle and $p_1, p_2, p_3$ are respectively altitudes
Give that $p_1, p_2, p_3$ are in AP
$\Rightarrow \quad \frac{2 \Delta}{a}, \frac{2 \Delta}{b}, \frac{2 \Delta}{c}$ are in $\mathrm{AP}$
$\Rightarrow \quad \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $\mathrm{AP}$
$\Rightarrow \quad a, b, c$ are in HP