What is my misstake (math)?

In the figure ABCD (se attached photo) the angles DAB and CDA are right angles. The length of side BC is 3 cm, the length of CD is 4 cm and the length of AD is 2 cm. And the problem is to compare the side AB to 6 cm and determine which quantity is greater, with Quantity one being AB and Quantity two being 6 cm and... show more In the figure ABCD (se attached photo) the angles DAB and CDA are right angles. The length of side BC is 3 cm, the length of CD is 4 cm and the length of AD is 2 cm.

And the problem is to compare the side AB to 6 cm and determine which quantity is greater, with Quantity one being AB and Quantity two being 6 cm and the choices are
A. Q1 is greater
B. Q2 is greater
C. Q1 = Q2
D. The information is insufficient

I got A. to be the right answer by dividing the figure into a rectangular with the sides AD and DC and a triangle with the sides AD BC and part of AB and then used pythagoras theorem to find the unknown side, sqrt(3^2-2^2) = sqrt(5) and then AB = DC + sqrt(5) = 4 + sqrt(5) and since sqrt(5) > sqrt(4) = 2 so AB = 4 + something greater than 2 and is therefor greater than 6.

But the answer is supposed to be D, information is insufficient. What is my mistake?
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