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Question Number 21231 by Tinkutara last updated on 16/Sep/17

$$\mathrm{Consider}\mathrm{the}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{four}\mathrm{triangles}$$$$\mathrm{obtained}\mathrm{by}\mathrm{drawing}\mathrm{the}\mathrm{diagonals}AC$$$$\mathrm{and}BD\mathrm{of}\mathrm{a}\mathrm{trapezium}ABCD.\mathrm{The}$$$$\mathrm{product}\mathrm{of}\mathrm{these}\mathrm{areas},\mathrm{taken}\mathrm{two}\mathrm{at}$$$$\mathrm{time},\mathrm{are}\mathrm{computed}.\mathrm{If}\mathrm{among}\mathrm{the}\mathrm{six}$$$$\mathrm{products}\mathrm{so}\mathrm{obtained},\mathrm{two}\mathrm{products}\mathrm{are}$$$$1296\mathrm{and}576,\mathrm{determine}\mathrm{the}\mathrm{square}$$$$\mathrm{root}\mathrm{of}\mathrm{the}\mathrm{maximum}\mathrm{possible}\mathrm{area}\mathrm{of}$$$$\mathrm{the}\mathrm{trapezium}\mathrm{to}\mathrm{the}\mathrm{nearest}\mathrm{integer}.$$

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