One leg of a right angel is 4 less than the other leg. the square of the hypotenuse of the right angel is 80. how long are the legs of the right triangle? show your work.

Sometimes these problems are easier to work if you consider the average of the two leg lengths. Call that "x".
.. (x -2)^2 +(x +2)^2 = 80 . . . . . . . by the Pythagorean theorem
.. x^2 -4x +4 +x^2 +4x +4 = 80 . . eliminate parentheses
.. 2x^2 +8 = 80 . . . . . . . . . . . . . . . simplify
.. x^2 = (80 -8)/2 = 36
.. x = √36 = 6
Legs are this value ±2.

The leg lengths are 4 and 8.

Were is the diagram?