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 Take Perpendicular Distances, Get One Side (Posted on 2007-07-08)
(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?

 See The Solution Submitted by K Sengupta Rating: 3.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 2 of 4 |
`Let A and B be the feet of the perpendiculars tosides PR and QR respectively. Using similar triangleswe get`
`  |SA|     |SA|     |PA|     |PR| - |AR|     |PR| - |SB| ------ = ------ = ------ = ------------- = -------------  |SB|     |AR|     |AS|         |SA|            |SA|`
`        or`
`         |SA|^2 + |SB|^2 |PR| = -----------------               |SB|`
`                  6^2 + 3^2Part (A): |PR| = ----------- = 15                      3`
`                  8^2 + 4^2Part (B): |PR| = ----------- = 20                      4`
` `

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

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