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Take Unit Length, Get PR (Posted on 2007-06-17) Difficulty: 3 of 5
The perpendicular from vertex P of the triangle PQR meets QR at the point S. A point T is located on PR such that QT=TR=RS=1.

What is the length of PR, given that Angle QPR=90o?

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution Solution | Comment 1 of 2

Applying the Pathagorean theorem to right triangles:
  PSQ: |PS|^2 + |SQ|^2 = |PQ|^2
                  or
       |PS|^2 + (|QR| - 1)^2 = |PQ|^2        (1)
  PSR: |PS|^2 + |SR|^2 = |PR|^2
                  or
       |PS|^2 + 1 = |PR|^2                   (2)
  QPR: |QP|^2 + |PR|^2 = |QR|^2
                  or
       |PQ|^2 + |PR|^2 = |QR|^2              (3)
  QPT: |QP|^2 + |PT|^2 = |QT|^2
                  or
       |PQ|^2 + (|PR| - 1)^2 = 1             (4)
Solving the equations (1)-(4) for |PR| we get
  |PR| = cube-root(2) 
 

  Posted by Bractals on 2007-06-17 13:26:44
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