(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 20070708 20:33:15 