Question 391000
picture the pentagon divided into ten congruent right triangles
___ by lines drawn from the midpoint of a side to the opposite vertex


the "central" angle of the right triangle (in the center of the pentagon) is 36º (360º / 10)


the length of the side of the triangle from the right angle to the center of the pentagon is D/2
___ this same side , added to the hypotenuse of the right triangle , equals C


(D / 2) + h = C


from trigonometry ___ (D / 2) / h = cos(36º) ___ (D / 2) / cos(36º) = h


substituting ___ (D / 2) + [(D / 2) / cos(36º)] = C


D{1 + [1 / cos(36º)]} = 2C


D = 2C / {1 + [1 / cos(36º)]}