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In triangle BAC, AD is perpendicular to BC, AB = 6 times the square root of 2, and DC = 2BD. What is the area of triangle ADC?

Mathematics
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|dw:1338085605509:dw|
The interesting thing about a 45-45-90 triangle is that if the sides are of length x, then the hypotenuse is x times the square root of 2. So for the triangle ABD, if the hypotenuse is 6 times the square root of 2, what is the length of AD and BD?
x?

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Other answers:

|dw:1338086273824:dw|True, but what is the value of x?
OH. IT'S SIX.
Right! So can you now calculate the area of the triangle ABC?
But one question, how do we know that BD and AD are congruent? ._.
OH. BECAUSE IT'S AN ISOSCELES TRIANGLE BECAUSE THE BASE ANGLES ARE CONGRUENT RIGHT?! :D
I forgot, my bad xP
Right!
Remember the angles of a triangle always have to add up to 180, so 180-(45+90)=45
OH. SO IS THE ANSWER 54?! :D
Area of a triangle =1/2 height by base\[A=\frac12(6)(12)=?\]
oh right. :o i forgot it was just triangle ADC.
so is it 36 then!? :o
Yep.
OMG THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D YOU'RE A LIFESAVER. YOU HELPED ME SO MUCH X)
You're very welcome. It is great to memorize the tricks of a 45-45-90 triangle and a 30-60-90 triangle. Nice shortcuts. This is a great website for this:http://library.thinkquest.org/20991/geo/stri.html
okay, thank you SO much x)

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