anonymous
  • anonymous
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
chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1338085605509:dw|
pfenn1
  • pfenn1
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?
anonymous
  • anonymous
x?

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pfenn1
  • pfenn1
|dw:1338086273824:dw|True, but what is the value of x?
anonymous
  • anonymous
OH. IT'S SIX.
pfenn1
  • pfenn1
Right! So can you now calculate the area of the triangle ABC?
anonymous
  • anonymous
But one question, how do we know that BD and AD are congruent? ._.
anonymous
  • anonymous
OH. BECAUSE IT'S AN ISOSCELES TRIANGLE BECAUSE THE BASE ANGLES ARE CONGRUENT RIGHT?! :D
anonymous
  • anonymous
I forgot, my bad xP
pfenn1
  • pfenn1
Right!
pfenn1
  • pfenn1
Remember the angles of a triangle always have to add up to 180, so 180-(45+90)=45
anonymous
  • anonymous
OH. SO IS THE ANSWER 54?! :D
pfenn1
  • pfenn1
Area of a triangle =1/2 height by base\[A=\frac12(6)(12)=?\]
anonymous
  • anonymous
oh right. :o i forgot it was just triangle ADC.
anonymous
  • anonymous
so is it 36 then!? :o
pfenn1
  • pfenn1
Yep.
anonymous
  • anonymous
OMG THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D YOU'RE A LIFESAVER. YOU HELPED ME SO MUCH X)
pfenn1
  • pfenn1
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
anonymous
  • anonymous
okay, thank you SO much x)

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