InterviewSolution
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InterviewSolution
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If A is the area and 2s is the sum of the sides of a triangle, thenA. `A le (s^(2))/(4)`B. `A le (s^(2))/(3sqrt3)`C. `A lt (s^(2))/(sqrt3)`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.` `rArr (s+(s-a) +(s-b)+(s-c))/(4)` `ge [s (s-a) (s-b) (s-c)]^(1//4)` `rArr (4s-2s)/(4) ge [A^(2)]^(1//4)` `rArr ((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)` or `(s)/(3) ge [(A^(2))/(s)]^(1//3) or (A^(2))/(s) le (s^(3))/(27) or A le (s^(2))/(3sqrt3)` |
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