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## xRAWRRx3 Group Title 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? 2 years ago 2 years ago

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1. xRAWRRx3 Group Title

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2. pfenn1 Group Title

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?

3. xRAWRRx3 Group Title

x?

4. pfenn1 Group Title

|dw:1338086273824:dw|True, but what is the value of x?

5. xRAWRRx3 Group Title

OH. IT'S SIX.

6. pfenn1 Group Title

Right! So can you now calculate the area of the triangle ABC?

7. xRAWRRx3 Group Title

But one question, how do we know that BD and AD are congruent? ._.

8. xRAWRRx3 Group Title

OH. BECAUSE IT'S AN ISOSCELES TRIANGLE BECAUSE THE BASE ANGLES ARE CONGRUENT RIGHT?! :D

9. xRAWRRx3 Group Title

I forgot, my bad xP

10. pfenn1 Group Title

Right!

11. pfenn1 Group Title

Remember the angles of a triangle always have to add up to 180, so 180-(45+90)=45

12. xRAWRRx3 Group Title

OH. SO IS THE ANSWER 54?! :D

13. pfenn1 Group Title

Area of a triangle =1/2 height by base$A=\frac12(6)(12)=?$

14. xRAWRRx3 Group Title

oh right. :o i forgot it was just triangle ADC.

15. xRAWRRx3 Group Title

so is it 36 then!? :o

16. pfenn1 Group Title

Yep.

17. xRAWRRx3 Group Title

OMG THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D YOU'RE A LIFESAVER. YOU HELPED ME SO MUCH X)

18. pfenn1 Group Title

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

19. xRAWRRx3 Group Title

okay, thank you SO much x)