let 'x' represent the length of the hypotenuse, x>0

1 leg of a right triangle is 6 units less than the length of the hypotenuse: x - 6, and x - 6>0, x>6

the other leg is 3 less than the length of the hypotenuse: x - 3, and x - 3>9, x>3

by using the Pythagorean Theorem we have:

(x - 6)^2 + (x - 3)^2 = x^2

by solving we find

X1 = 15 units

x2 = 3 units

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x = 3 units is not a solution because x - 6 = 3 - 6 = -3 is negative

for the hypotenuse equal to 15 units the legs are:

15 - 3 = 12 units

15 - 6 = 9 units

the 3 sides of the triangle are: the hypotenuse is 15 units, the legs are 12 and 9 units.