SOLUTION: What is the largest possible area, in square centimeters, of a right triangle with one side of length 12 cm and another side of length 20 cm?

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Question 1141777: What is the largest possible area, in square centimeters, of a right triangle with one side of length 12 cm and another side of length 20 cm?
Answer by ikleyn(52788) About Me  (Show Source):
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There are two and only two possibilities.


1.  12 cm and 20 cm are the legs.

    Then the area is  %281%2F2%29%2A12%2A20 = 120 cm^2.




2.  12 cm is one of the two legs and 20 cm is the hypotenuse.


    Then the other leg is  16 cm   (recall the 3-4-5 right angled triangle !),

     and the area is  %281%2F2%29%2A12%2A16 = 12*8 = 96 cm^2.


ANSWER.  The largest area under the question is 120 cm^2.


Answered, solved and completed.