MathDB

In rectangle

ABCD

, AD \equal{} 1,

P

is on

\overline{AB}

, and

\overline{DB}

and

\overline{DP}

trisect

\angle ADC

. What is the perimeter of

\triangle BDP

? [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

",A,NW); label("

B

",B,NE); label("

C

",C,SE); label("

D

",D,SW); label("

P

",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}

7

Problems(1)