Join D and B
DCB is an right angle triangle
DB^2= CD^2 +BC^2
=9 +16=25
or DB=5
Also, DB^2= AB^2 + AD^2
25=AB^2 + 1
AB^2 = 24
AB= 2*(6^0.5)

Hi All,

We're asked for the length of AB in quadrilateral ABCD.

When dealing with 'weird' shapes, it often helps to break the shape down into 'pieces' that are easier to deal with. Here, if you draw a line from B to D, you will from 2 RIGHT TRIANGLES.

Triangle BCD has legs of 3 and 4, so it's a 3/4/5 right triangle.
Triangle BAD then has a leg of 1 and a hypotenuse of 5. We can use the Pythagorean Formula to find the missing leg...

1^2 + B^2 = 5^2
1 + B^2 = 25
B^2 = 24

From here, if we square-root both sides, we'll have...
B = √24
B = 2√6

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Solution

Given:

• AD= 1
• CD=1
• BC=1

To Find:

• The length of AB.

Approach and Working:

Let us join the points B and D.



Since ∆ BCD is a right -angled triangle, we can apply Pythagoras theorem in ∆ BCD.

• Thus, \(BD^2\) = \(CD^2\) +\(BC^2\)

o \(BD^2\) = \(4^2\) +\(3^2\) = 16+9 = 25
o \(BD^2\) = 25

 BD=5

Now, we can apply Pythagoras theorem in triangle ABD.

• Hence, \(BD^2\) =\(AD^2\) + \(AB^2\)

o 25 = 1 + \(AB^2\)

 \(AB^2\) = 24
 AB = √24 = 2√6.

Hence, option C is the correct answer.

Correct Answer: Option C
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