You are on a trip to one of the Cartesian Islands. In the cellar of your cabin you have found an old map that claims to hold the secret location of buried treasure. The map shows four trees at locations A, B, C. and D. The trees at A and D are along a road that runs through the island. The tree at B is directly north of the tree at A, and the tree at C is directly north of the tree at D.

The map's directions say to trace a path from the tree at B to the tree at D, and to do the same for the trees at A and C. The treasure is buried halfway between the intersection of these paths and the road. Because three small lakes dot the island, you are only able to measure the distances between B and D, A and C, and A and D:

To find the location of the treasure, you must determine the distance from E to the road and then walk half that distance from E. How far is F from the road?