## xRAWRRx3 3 years ago 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?

1. xRAWRRx3

|dw:1338085605509:dw|

2. 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?

3. xRAWRRx3

x?

4. pfenn1

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

5. xRAWRRx3

OH. IT'S SIX.

6. pfenn1

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

7. xRAWRRx3

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

8. xRAWRRx3

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

9. xRAWRRx3

10. pfenn1

Right!

11. pfenn1

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

12. xRAWRRx3

OH. SO IS THE ANSWER 54?! :D

13. pfenn1

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

14. xRAWRRx3

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

15. xRAWRRx3

so is it 36 then!? :o

16. pfenn1

Yep.

17. xRAWRRx3

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

18. 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

19. xRAWRRx3

okay, thank you SO much x)