UPSC NDA Math Model Paper 5

Let's say that the sides of the triangle are a, b and c and the altitudes corresponding to them are p, q and r respectively.
Since, the area of the triangle is same, we have:

1

2

×a×p=

1

2

×b×q=

1

2

×c×r
⇒a×p=b×q=c×r=k (suppose)
⇒a=

k

p

,b=

k

q

,c=

k

r

Since the altitudes p, q and r are given to be in AP, we can say that a, b, c are in Harmonic Progression (HP).