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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?

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  1. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    10?

  3. KingGeorge
    • 3 years ago
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    Perfect. Now what's the formula for area of a triangle?

  4. xRAWRRx3
    • 3 years ago
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    A = 1/2 base times height?

  5. KingGeorge
    • 3 years ago
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    Right on. What's the distance between (7, 2) and (7, b) in terms of b?

  6. KingGeorge
    • 3 years ago
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    And assuming b is positive.

  7. xRAWRRx3
    • 3 years ago
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    I'm not sure, that's the part I don't get D: I don't know how to solve it.

  8. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    yeah, that's what I tried to do.

  10. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    mhmm, then?

  12. KingGeorge
    • 3 years ago
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    One last thing. What's the base and the height of the triangle?

  13. xRAWRRx3
    • 3 years ago
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    well, the base would be 10 since we figured that out and aren't we trying to find the height right now?

  14. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    It's perpendicular?

  16. KingGeorge
    • 3 years ago
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    Right.

  17. KingGeorge
    • 3 years ago
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    |dw:1338696349644:dw|Can you tell me what the area of this triangle is?

  18. xRAWRRx3
    • 3 years ago
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    5b - 10? ._. idk...

  19. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    well, they gave it to us that the area is 45.

  21. dpaInc
    • 3 years ago
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    can i suggest another method?

  22. KingGeorge
    • 3 years ago
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    Go ahead.

  23. xRAWRRx3
    • 3 years ago
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    ohmigosh ._. what is that? ._.

  24. xRAWRRx3
    • 3 years ago
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    sorry, but I don't think I learned that LOL

  25. KingGeorge
    • 3 years ago
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    Back to the first way then.

  26. xRAWRRx3
    • 3 years ago
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    LOL sorry, dpalnc :(

  27. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    i don't know why but I got 9.4....

  29. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    Can you solve the equation \[45=5(b-2)\]for \(b\)?

  31. xRAWRRx3
    • 3 years ago
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    yeahh so then that would become: 45 = 5b -10.. OH. OKAY HOLD ON. I MADE A MISTAKE LOL

  32. xRAWRRx3
    • 3 years ago
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    B = 11 !!!

  33. KingGeorge
    • 3 years ago
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    Perfect. Great job.

  34. xRAWRRx3
    • 3 years ago
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    OHMIGOSH THANK YOU SO MUCH :D YOU HELPED ME SO MUCH THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU :D

  35. KingGeorge
    • 3 years ago
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    You're welcome :)

  36. dpaInc
    • 3 years ago
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    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

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