The length of the longer leg is 35 inches.
Let x be the length of the shorter leg. Then the length of the longer leg is x + 3. We can use the Pythagorean Theorem to solve for x:
x^2 + (x + 3)^2 = 65^2
Expanding the left side of the equation, we get:
x^2 + x^2 + 6x + 9 = 4225
Combining like terms, we get:
2x^2 + 6x - 4216 = 0
Factoring the expression, we get:
(2x - 64)(x + 66) = 0
Therefore, x = 32 or x = -66. Since the length of a leg cannot be negative, we know that the length of the shorter leg is 32 inches and the length of the longer leg is 32 + 3 = 35 inches.