Let R be the area of rectangle ABCD and
T the area of triangle APQ (where P and
Q are points on sides BC and CD of ABCD respectively).

What is the minimal value of |BP|+|DQ|
in terms of R and T?

Note: R and T are constants with 0 < T ≤ R/2.
Therefore, |BP| and |DQ| are not independent variables
(i.e. if P varies between B and C, then Q
must vary between C and D such that T
stays constant).  

(In reply to solution by xdog)

Your solution doesnt match what I found using Geometers Sketchpad, but I found your error.

x + (R-2T)/x is a minimum when x = sqrt(R-2t), not x+y as you stated.

x + y then simplifies to 2*sqrt(R-2t).

An interesting result, which I hadnt noticed is that this means x and y are precisely equal.

Posted by Jer on 2010-10-14 15:15:37