3. (3 points) As shown in the right figure, the length of rectangle $A B C D$ is 6 cm, and the width is 2 cm. A line segment $A E$ is drawn through point $A$ to divide the rectangle into two parts, one part being a right triangle, and the other part being a trapezoid. If the area of the trapezoid is 3 times the area of the right triangle, then, the difference between the perimeter of the trapezoid and the perimeter of the right triangle is $\qquad$ cm.
3. (3 points) As shown in the right figure, the length of rectangle $A B C D$ is 6 cm, and the width is 2 cm. A line segment $A E$ is drawn through point $A$, dividing the rectangle into two parts, one being a right triangle and the other a trapezoid. If the area of the trapezoid is 3 times the area of the right triangle, then, the difference between the perimeter of the trapezoid and the perimeter of the right triangle is $\qquad$ cm.

【Solution】According to the problem, $S$ trapezoid $A B D E = S \triangle A C E \times 3$,
which means $(A B + E D) \times B D \div 2 = A C \times C E \div 2 \times 3$,
or $(A B + E D) \times 2 \div 2 = 2 \times C E \div 2 \times 3$.
So, $A B + E D = C E \times 3$,
From this, we know that point $E$ is the midpoint of the base of rectangle $A B C D$, so $C E = E D = 3$ cm;
Therefore, $A B + E D - C E = 6 + 3 - 3 = 6$ (cm);
Answer: The difference between the perimeter of the trapezoid and the perimeter of the right triangle is 6 cm.
So the answer is: 6.