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In triangleABC ,Delta=6, abc=60, r=1 The...

In `triangleABC` ,`Delta=6`, `abc=60`, `r=1` Then the value of `1/a+1/b+1/c` is nearly (a) 0.5 (b) 0.6 (c) 0.4 (d) 0.8

A

`0.5`

B

0.6

C

0.4

D

0.8

Text Solution

Verified by Experts

The correct Answer is:
D
`r=(Delta)/(s) =1 rArr s =6`
`:. (s-a) (s-b)(s-c) = s`
`rArr s^(3) - (a +b +c)s^(2) + (ab + bc + ca)s -abc = s`
`rArr 6^(3) - 12 xx 36 + (ab + bc +ca) - 60 = 6`
`rArr ab + bc + ca = 47`
`:' (1)/(a) + (1)/(b) + (1)/(c) = (47)/(60) = 0.8` (nearly)
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