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Pythagoras and algebra

  1. Mar 21, 2016 #1
    • Member warned about posting with no effort shown
    1. The problem statement, all variables and given/known data
    In a diagram, P, Q and R lie on a straight line and angle SQR is a right angle. The lengths PS, SR and RP are a, b and c cm respectively and QR is x cm.

    Use algebra to show that x = (b^2 + c^2 - a^2) / 2c

    2. Relevant equations and attempt at a solution

    Do I need to use Pythagoras for this question? I need a prompt, a little help please...
     

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    Last edited: Mar 21, 2016
  2. jcsd
  3. Mar 21, 2016 #2

    SteamKing

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    Beats me. Do you have a diagram to refer to? If not, you should make one, based on the description of the points.

    Since there is a right angle involved, I would keep Pythagoras handy, nevertheless.
     
  4. Mar 21, 2016 #3
    I have attached a picture of the triangle in question... Hope it worked...
     
  5. Mar 21, 2016 #4

    HallsofIvy

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    Drawing a line from the right angle perpendicular to the hypotenuse divides the original right angle into two triangles both similar to the original triangle.
     
  6. Mar 22, 2016 #5

    ehild

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    Yes, you can solve the problem by using Pythagoras' Theorem for both the yellow and blue triangles.

    upload_2016-3-22_6-32-52.png
     
  7. Mar 22, 2016 #6
    Got it!
    After some working I got...

    a^2 - c^2 +2cx -x^2 = b^2 - x^2
    which simplifies to:
    x = (b^2 + c^2 - a^2) / 2c

    Thanks ehild I equated the m
     
  8. Mar 23, 2016 #7

    ehild

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    well done!
     
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