DB and DP trisect angle ADC, so m∠ADP = m∠PDB = m∠BDC = 90° / 3 = 30°
∠ABD and ∠BDC are alternate interior angles, so they have the same measure.
If we draw a line from P to BD that is perpendicular to side BD, we will have congruent triangles.
The angle measures of these triangles are 30°, 60°, and 90° .
The side opposite the 60° angle = 1 , so
the side opposite the 90° angle = 2 / √3
perimeter of triangle BDP = 2 + 2/√3 + 2/√3 = 2 + 4/√3 = 2 + 4√3 / 3
2 + 4 + 3 + 3 = 12