The radii `r_1, r_2,r_3` of the escribed circles of the triangle `A B C` are in H.P. If the area of the triangle is `24 c m^2a n d` its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

Options

A. 10
B. 9
C. 8
D. none of these

Answer

A

Explanation

Given `r_(1), r_(2), r_(3)` are in H.P. Thus,
a, b, c are in A.P
and `a + b + c = 24 = 2s`
or `ab + b = 24`
or `b = 8`
`rArr c = 16 -a`
Also given `sqrt(s(s-a)(s-b)(s-c)) = 24`
or `sqrt(12(12 -a) (12-8) (a-4)) = 24`
or `(12 -a) (a-4) = 12`
or `a^(2) - 16a + 16a + 60 = 0 rArr a = 6, 10`