InterviewSolution
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InterviewSolution
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If A is the area and 2s the sum of the sides of a triangle,thenA. `Ale (s^2)/(4)`B. `Ale(s^2)/(3sqrt(3))`C. `Alt (s^2)/(sqrt(3)`D. none of these |
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Answer» Correct Answer - A::B We have `2s = a + b + c` `A^(2) = s (s - a) (s - b)(s - c)` Now, `A.M. ge G.M` `implies (s + (s - a) + (s - b) + (s - c))/(4) ge [s(s-a)(s-b)(s-c)]^(1//4)` `implies (4s - 2s)/(4) ge [A^(2)]^(1//4)` `implies s//2 ge A^(1//2)` or `A le s^(2)//4` Also, `((s - a) + (s - b) + (s - c))/(3) ge [(s - a) (s - b) (s - c)]^(1//3)` `implies (s)/(3) ge [(A^(2))/(s)]^(1//3)` or `(A^(2))/(s) le (s^(3))/(27)` or `A le (s^(2))/(3sqrt(3))` |
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