Question 7In rectangle $ABCD,$ $AD = 1,$ $P$ is on $\overline{AB},$ and $\overline{DB}$ and $\overline{DP}$ trisect $\angle ADC.$ What is the perimeter of $\triangle BDP?$ $3 + \dfrac{\sqrt3}{3}$$2 + \dfrac{4\sqrt3}{3}$$2 + 2\sqrt2$$\dfrac{3 + 3\sqrt5}{2}$$2 + \dfrac{5\sqrt3}{3}$
