If area of a triangle is 2 sq. units, then find the value of the product of the arithmetic mean of the lengths of the sides of a triangle and harmonic mean of the lengths of the altitudes of the triangle.

Explanation

Let `a,b and c` are the sides and `h_1,h_2 and h_3` are the lengths of the altitudes.

Then,

`ah_1 = bh_2 = ch_3 = 2Delta`

`=>1/h_1+1/h_2+1/h_3 = (a+b+c)/(2Delta)`

`=>2Delta = (a+b+c)/(1/h_1+1/h_2+1/h_3)`

`=>2Delta = (a+b+c)/3**3/(1/h_1+1/h_2+1/h_3)`

Now, it is given that `Delta = 2` square units

`:. 2*2 = (a+b+c)/3**3/(1/h_1+1/h_2+1/h_3)`

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