(A) In a right angled triangle PQR, an altitude RS is drawn from the vertex R of the right angle. The respective perpendicular distances of the point S from the sides PR and QR are 6 and 3.

Determine the length of PR.

(B) What would have been the length of PR if the respective perpendicular distances of the point S from the sides PR and QR were 8 and 4?

Let A and B be the feet of the perpendiculars to
sides PR and QR respectively. Using similar triangles
we get

  |SA|     |SA|     |PA|     |PR| - |AR|     |PR| - |SB|
 ------ = ------ = ------ = ------------- = -------------
  |SB|     |AR|     |AS|         |SA|            |SA|

        or

         |SA|^2 + |SB|^2
 |PR| = -----------------
               |SB|

                  6^2 + 3^2
Part (A): |PR| = ----------- = 15
                      3

                  8^2 + 4^2
Part (B): |PR| = ----------- = 20
                      4

Posted by Bractals on 2007-07-08 20:33:15