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xRAWRRx3

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?

  • one year ago
  • one year ago

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  1. xRAWRRx3
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    |dw:1338085605509:dw|

    • one year ago
  2. pfenn1
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    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?

    • one year ago
  3. xRAWRRx3
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    x?

    • one year ago
  4. pfenn1
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    |dw:1338086273824:dw|True, but what is the value of x?

    • one year ago
  5. xRAWRRx3
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    OH. IT'S SIX.

    • one year ago
  6. pfenn1
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    Right! So can you now calculate the area of the triangle ABC?

    • one year ago
  7. xRAWRRx3
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    But one question, how do we know that BD and AD are congruent? ._.

    • one year ago
  8. xRAWRRx3
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    OH. BECAUSE IT'S AN ISOSCELES TRIANGLE BECAUSE THE BASE ANGLES ARE CONGRUENT RIGHT?! :D

    • one year ago
  9. xRAWRRx3
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    I forgot, my bad xP

    • one year ago
  10. pfenn1
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    Right!

    • one year ago
  11. pfenn1
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    Remember the angles of a triangle always have to add up to 180, so 180-(45+90)=45

    • one year ago
  12. xRAWRRx3
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    OH. SO IS THE ANSWER 54?! :D

    • one year ago
  13. pfenn1
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    Area of a triangle =1/2 height by base\[A=\frac12(6)(12)=?\]

    • one year ago
  14. xRAWRRx3
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    oh right. :o i forgot it was just triangle ADC.

    • one year ago
  15. xRAWRRx3
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    so is it 36 then!? :o

    • one year ago
  16. pfenn1
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    Yep.

    • one year ago
  17. xRAWRRx3
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    OMG THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D YOU'RE A LIFESAVER. YOU HELPED ME SO MUCH X)

    • one year ago
  18. pfenn1
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    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

    • one year ago
  19. xRAWRRx3
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    okay, thank you SO much x)

    • one year ago
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