A right triangle has a hypotenuse with the length equal to 12 cm.

What is the greatest possible area of this triangle ?

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Form is valid through February 2019


Dear friends of the site! Thank you for your solutions! The first to send a correct one was James. To him our best congrats!   Here is the solution: The hypotenuse is the diameter of the circumcircle. This the greatest possible height is R=6 cm. Thus the maximal are is 36 cm^2. And now welcome to our March Problem Serge Hazanov