Rectangle
Source:
March 3, 2006
geometryrectangleperimetertrigonometry
Problem Statement
In rectangle , AD \equal{} 1, is on , and and trisect . What is the perimeter of ?
[asy]unitsize(2cm);
defaultpen(linewidth(.8pt));
dotfactor=4;pair D=(0,0), C=(sqrt(3),0), B=(sqrt(3),1), A=(0,1), P=(sqrt(3)/3,1);
pair[] dotted={A,B,C,D,P};draw(A--B--C--D--cycle);
draw(B--D--P);
dot(dotted);
label("",A,NW);
label("",B,NE);
label("",C,SE);
label("",D,SW);
label("",P,N);[/asy] (A)\ 3 \plus{} \frac {\sqrt3}{3} \qquad(B)\ 2 \plus{} \frac {4\sqrt3}{3}\qquad(C)\ 2 \plus{} 2\sqrt2\qquad(D)\ \frac {3 \plus{} 3\sqrt5}{2} \qquad(E)\ 2 \plus{} \frac {5\sqrt3}{3}