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solutions of triangle
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4 sol)  2=s(s-a)(s-b)(s-c) 2/s=(s-a)(s-b)(s-c)= (s-a)(s-b)*(s-b)(s-c)*(s-c)(s-a).......(1) using A.M>=G.M, (S-a)+(s-b)/2>= (s-a)(s-b) {[(b+c-a)/2]+[(a+c-b)/2]}/2>=(s-a)(s-b)c/2>=(s-a)(s-b) (s-a)(s-b)<=c/2.......(2) similarly, (s-b)(s-c)<=a/2.......(3)(s-c)(s-a)<=b/2........(4)using the results (2), (3) &(4) in (1) 2/s<=(c/2)(a/2)(b/2) 2<=s(abc/8)<=[(a+b+c)/2](abc/8)=(a+b+c)(abc)/16hence,
<=(1/4)(a+b+c)(abc) |
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