Carcass wrote:

In quadrilateral ABCD above, what is the length of AB ?
A.
√26B.
2√5C.
2√6D.
3√2E.
3√3First add a line to join B and D:

If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem.

Either way, we'll see that the triangle's hypotenuse (BD) must have length 5
Now, when we focus on the red right triangle, we can . . .

. . . apply the Pythagorean Theorem to write: x² + 1² = 5²
Simplify: x² + 1 = 25
So: x² = 24
So: x = √24 = √[(4)(6)] = (√4)(√6) = 2√6
Answer: C
Cheers,
Brent