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[@9990010]

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[@Mathsandolympiad]

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[@Ramkabharosa]

bc = 200 & ca = 300 implies b/a = 2/3. So a = 3b/2. Since ab = 100,
(3b/2).b = 100 which implies b² = 200/3 = 600/9. So b = 10√6/3.
∴ a = 3(10√6/3)/2 = 5√6 & c = 300/a = 300/5√6 = 300√6/30 = 10√6.
Hence a + b + c = 5√6 + 10√6/3 + 10√6 = (55√6)/3 .