Need help with a ratio property of intercepts problem?

Question

A rectangular box sits on a train luggage rack as shown with the point C touching the wall. P, the point in contact with the rack is the midpoint of AD. If D is 8 cm from the wall and P the edge of the rack is 20 cm from the wall find how far A is from the wall.

Draw parallels to the wall throught A, P and D.

http://oi47.tinypic.com/s4qis0.jpg <- Diagram

The answer is 32 cm but I can't work it out. Please show the working out.

Answer 1

 

Distance between wall and D is 8 cm

Distance between wall and P is 20 cm

From the above geometry Distance between P and D is 20-8=12 cm

P is the midpoint,therefore AP=PD=x=12 cm

Distance between wall and A is 20+x

Substitute 12 cm for x in above 20+x=20+12=32 cm

32 cm far A is from the wall

 I hope that helps u