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 Take Unit Length, Get PR (Posted on 2007-06-17)
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 | 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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