## xRAWRRx3 Group Title Please help :( A right triangle with area 45 has vertices at (-3, 2), (7, 2), and (7, b), where b > 0. What is the value of b? 2 years ago 2 years ago

1. KingGeorge Group Title

If you were to graph this, you could probably see what to do. |dw:1338695720852:dw|You want a point on that line so that the area is 45. Can you tell me what the distance is between (-3, 2) and (7, 2)?

2. xRAWRRx3 Group Title

10?

3. KingGeorge Group Title

Perfect. Now what's the formula for area of a triangle?

4. xRAWRRx3 Group Title

A = 1/2 base times height?

5. KingGeorge Group Title

Right on. What's the distance between (7, 2) and (7, b) in terms of b?

6. KingGeorge Group Title

And assuming b is positive.

7. xRAWRRx3 Group Title

I'm not sure, that's the part I don't get D: I don't know how to solve it.

8. KingGeorge Group Title

Well, there's two ways to look at it. The easy way, or the hard way. The hard way uses the distance formula. $\sqrt{(b-2)^2+(7-7)^2} =\sqrt{(b-2)^2}=b-2$

9. xRAWRRx3 Group Title

yeah, that's what I tried to do.

10. KingGeorge Group Title

The easy way is to look at the graph. It's a straight vertical line from (7, 2) to (7, b), so the distance is just $$b-2$$. Once again, assuming b is greater than 2.

11. xRAWRRx3 Group Title

mhmm, then?

12. KingGeorge Group Title

One last thing. What's the base and the height of the triangle?

13. xRAWRRx3 Group Title

well, the base would be 10 since we figured that out and aren't we trying to find the height right now?

14. KingGeorge Group Title

We know that the distance from (7, 2) to (7, b) is b-2, and it's a vertical line. What does that tell you about the height of the triangle?

15. xRAWRRx3 Group Title

It's perpendicular?

16. KingGeorge Group Title

Right.

17. KingGeorge Group Title

|dw:1338696349644:dw|Can you tell me what the area of this triangle is?

18. xRAWRRx3 Group Title

5b - 10? ._. idk...

19. KingGeorge Group Title

In this triangle, the base is of length 10, and the height is b-2. Using the formula for the area of a triangle, what do you get as the area?

20. xRAWRRx3 Group Title

well, they gave it to us that the area is 45.

21. dpaInc Group Title

can i suggest another method?

22. KingGeorge Group Title

23. xRAWRRx3 Group Title

ohmigosh ._. what is that? ._.

24. xRAWRRx3 Group Title

sorry, but I don't think I learned that LOL

25. KingGeorge Group Title

Back to the first way then.

26. xRAWRRx3 Group Title

LOL sorry, dpalnc :(

27. KingGeorge Group Title

You're given that the area is 45, the base is of length 10, and the height is b-2. Now use your formula of $A=\frac{1}{2}bh$with $$b=10$$ and $$h=b-2$$ (those are different $$b$$'s). What do you get?

28. xRAWRRx3 Group Title

i don't know why but I got 9.4....

29. KingGeorge Group Title

I don't know why either :P You should get $A=45=\frac{1}{2}\cdot10\cdot(b-2)=5\cdot(b-2)$

30. KingGeorge Group Title

Can you solve the equation $45=5(b-2)$for $$b$$?

31. xRAWRRx3 Group Title

yeahh so then that would become: 45 = 5b -10.. OH. OKAY HOLD ON. I MADE A MISTAKE LOL

32. xRAWRRx3 Group Title

B = 11 !!!

33. KingGeorge Group Title

Perfect. Great job.

34. xRAWRRx3 Group Title

OHMIGOSH THANK YOU SO MUCH :D YOU HELPED ME SO MUCH THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D

35. KingGeorge Group Title

You're welcome :)

36. dpaInc Group Title

here is the thing that i was suggesting to find the area of a triangle using matrices: http://www.youtube.com/watch?v=a5C_I5Fywfo