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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 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?

 

I know this has already been answered, but it was wrong. 396 is not the answer.

 Apr 7, 2022
 #1
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The only triangle that works is the triangle with legs 4 and 4, so the answer is 4*4/2 = 8.

 Apr 7, 2022
 #2
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I think there is a mistake in your question! Why? Because:

 

[A * B]/2  CANNOT EQUAL (A + B), and A and B be legs of a right triangle. You can have: A=3 and B=6 and

 

[6 x 3]/2 ==6 + 3. But 6, and 3 CANNOT be legs of a right triangle, because their sum SQUARED, 6^2 + 3^2 ==PERFECT square. In this case, they wqual (45), which not a pefect square.

 

Your question should read: "A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to [TWICE (OR 3 TIMES)] the number of units in the sum of the lengths of its legs.

 Apr 7, 2022

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