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ankaua
The answer is B.

We do have two properties of a right triangle when we have an altitude drawn from the right angle to hypotenuse:

1) The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.
In terms of the right triangle in question: BD=\sqrt{AD*DC}

2) If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
In terms of the right triangle in question: AB =\sqrt{AD*AC}

So, to find AD, we need either AC or BD and DC

Quote:
(1) BD=2 \sqrt{5}
Not sufficient. We are given altitude, in order to find AD we need to have also DC as given.

Quote:
(2) DC=5
Sufficient.


ankaua ,
Already Given is AB = 6
In statement 1 , They have given one side of Perpendicular side of Triangle i.e. BD=2 Square root 5 , Also angle BDA is given i.e. 90 degree
By Pythagoras ,
You can find AD.
As AD^2 + BD^2 = AB^2
By above you can find AD.
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rajatchopra1994
you are right! I've concentrated on more complex property and overlooked such an easy possibility. Appreciate!
So, it seems the answer will be D?
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rajatchopra1994
you are right! I've concentrated on more complex property and overlooked such an easy possibility. Appreciate!
So, it seems the answer will be D?

With Statement 2 alone,
2 cases are possible, If it is 45-45-90 or 30-60-90
Therefore, length AD can have 2 values.
Solving ankaua By Your method, Statement 2 is sufficient

IMO D

Regards,
Rajat Chopra
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rajatchopra1994,
sure, let's wait for QA! Anyway, thanks again for spotting an error in my reasoning! Also, you encouraged me to solve B in an alternative way, using properties of similar thiangles! :)
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