Search any question & find its solution
Question:
Answered & Verified by Expert
If the altitude of a triangle are in arithmetic progression, then the sides of the triangles are in
Options:
Solution:
1516 Upvotes
Verified Answer
The correct answer is:
$\mathrm{HP}$
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
$$
\Delta=\frac{1}{2} a p_1=\frac{1}{2} b p_2=\frac{1}{2} c p_3
$$
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
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.