The radii `r_(1), r_(2), r_(3)` of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is `24 cm^(2)` and its perimeter i

Monjur Alahi

The radii `r_(1), r_(2), r_(3)` of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is `24 cm^(2)` and its perimeter is 24 cm, then the length of its largest side is
A. 10
B. 9
C. 8
D. none of these


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Salim Ahmed Kawsar

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Correct Answer - A
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`

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