## xRAWRRx3 3 years ago 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?

1. KingGeorge

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

10?

3. KingGeorge

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

4. xRAWRRx3

A = 1/2 base times height?

5. KingGeorge

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

6. KingGeorge

And assuming b is positive.

7. xRAWRRx3

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

8. KingGeorge

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

yeah, that's what I tried to do.

10. KingGeorge

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

mhmm, then?

12. KingGeorge

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

13. xRAWRRx3

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

14. KingGeorge

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

It's perpendicular?

16. KingGeorge

Right.

17. KingGeorge

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

18. xRAWRRx3

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

19. KingGeorge

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

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

21. dpaInc

can i suggest another method?

22. KingGeorge

23. xRAWRRx3

ohmigosh ._. what is that? ._.

24. xRAWRRx3

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

25. KingGeorge

Back to the first way then.

26. xRAWRRx3

LOL sorry, dpalnc :(

27. KingGeorge

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

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

29. KingGeorge

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

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

31. xRAWRRx3

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

32. xRAWRRx3

B = 11 !!!

33. KingGeorge

Perfect. Great job.

34. xRAWRRx3

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

35. KingGeorge

You're welcome :)

36. dpaInc

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