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A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to twice the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right triangles?

 

This isn't the first time somebody posted this question but the last answer was incorrect.

 May 20, 2023
 #1
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I could find only 6 such right triangles as follows:

 

         A     B   H

1  = (16, 12, 20)
2  = (12, 16, 20)
3  = (24, 10, 26)
4  = (10, 24, 26)
5  = (40, 9, 41)
6  = (9, 40, 41)

 

 

Their total areas =792

 May 20, 2023
 #2
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Incorrect, the answer is 118.

 May 22, 2023

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