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Mathematical Marathon No. 1

Olympiads

Mathematical marathon rules:
1) New task should be posted by user who solved the last one task.
2) It is necessary to write decisions, formulas, drawings, graphs. Only answers are not allowed.
3) Since it is olympiadic math section, the tasks must be complex, requiring knowledge.
4) If no one solves the task, the solution should be posted by the author.
5) If the author does not provide a solution after three days, the new task can be uploaded by anyone who wants.

Last time edited 2017-09-27

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First task!
The sum of the lengths of the three sides of a right-angled triangle is equal to 18 and the sum of the squares of the lengths of the three sides is equal to 128. What is the area of the triangle?

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