In rectangle ABCD, the bisector of angle D intersects side AB at point P. Line AP is 6 times less than line BP.

In rectangle ABCD, the bisector of angle D intersects side AB at point P. Line AP is 6 times less than line BP. Find the sides of a rectangle if its perimeter is 72 centimeters.

Let’s denote the segment AP as x cm, then BP = 6x. After drawing the bisector, a right-angled triangle ADP was formed, which is also isosceles, since the bisector divided the angle of 90 degrees into angles of 45. Then the side AD = AP = x cm. Knowing the perimeter, we get the equation:
x + 6x + x + x + 6x + x = 72
16 x = 72
x = 4.5
4.5 + 4.5 * 6 = 31.5
Answer: 31.5 cm and 4.5 cm