If the altitudes of a triangle are in arithme | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In $	riangle ABC$,let $a, b, c$ be the side lengths and $p_1, p_2, p_3$ be the corresponding altitudes.We know that the area $\Delta = \frac{1}{2

Vedclass · Accepted Answer

$HP$

Vedclass · Answer

(B) In $	riangle ABC$,let $a, b, c$ be the side lengths and $p_1, p_2, p_3$ be the corresponding altitudes.We know that the area $\Delta = \frac{1}{2} a p_1 = \frac{1}{2} b p_2 = \frac{1}{2} c p_3$.This implies $p_1 = \frac{2\Delta}{a}$,$p_2 = \frac{2\Delta}{b}$,and $p_3 = \frac{2\Delta}{c}$.Given that $p_1, p_2, p_3$ are in $AP$,we have $\frac{2\Delta}{a}, \frac{2\Delta}{b}, \frac{2\Delta}{c}$ in $AP$.Dividing by $2\Delta$,we get $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $AP$.By definition,if the reciprocals of terms are in $AP$,then the terms themselves are in $HP$.Therefore,$a, b, c$ are in $HP$.

If the altitudes of a triangle are in arithmetic progression,then the sides of the triangle are in

Similar Questions

If $(h, k)$ is the image of the point $(2, -3)$ with respect to the line $5x - 3y = 2$,then $h + k$ is equal to

An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of the hydrogen atom. The wave number of the emitted radiation ($R =$ Rydberg's constant) will be

If the charge on a body is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The original charge on the body in coulomb is

The volume of one mole of the gas is changed from $V$ to $2 V$ at constant pressure $p$. If $\gamma$ is the ratio of specific heats of the gas,what is the change in internal energy of the gas?

Newton's law of cooling is a special case of

Vedclass Test Series

Exam Paper Generator

Online Exam Module