SOLUTION: If area of triangle is 2√2 unit.then least value of s (semi perimeter) is.........
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Question 841323: If area of triangle is 2√2 unit.then least value of s (semi perimeter) is.........
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Intuitively, the perimeter should be maximized when the triangle is equilateral, but it seems much harder to prove. By AM-GM, we have
 + (s-b) + (s-c)}{4} \ge \sqrt[4]{s(s-a)(s-b)(s-c)})
The RHS is a constant, and the LHS is equal to s/2 (since a+b+c = 2s). However the equality case cannot occur since this would imply s = s-a = s-b = s-c, which gives a = b = c = 0.
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