In a hotel bathroom, the tiles on the floor are 4" squares. There are similar tiles on the wall. The door open

Question

In a hotel bathroom, the tiles on the floor are 4" squares. There are similar tiles on the wall. The door opens into the bathroom with the hinge on the right side of the door frame. The door frame extends 2" from the adjacent wall (or in other words, the door hinge is 2" from the corner). The center of a rubber bumper on the end of a 1/2" long door stop contacts the adjacent wall 1" from the end of the fourth tile from the corner. Directly opposite the rubber bumper is the screw for attaching the door stop to the door.



How far from the hinge is the center of the screw hole for the rubber bumper? State you answer to the nearest 1/16th of an inch.

Answer 1

You're looking at a very thin quadrilateral. Two sides of length 2 inches and 15 inches are perpendicular. A third side (opposite the 15" side) has unknown length that you are solving for. The fourth side is perpendicular to something, and is 1/2" long.

That "something" logically should be the unknown side, but the question-writer could have had a brain cramp and meant the 15" side instead.

If the question is meant the logical way, draw the diagonal of the quadrilateral that doesn't go through the two right angles. It then is the hypoteneuse of two different right triangles. One has sides 2" and 15". Use the Pythagorean Theorem to compute its length. The other has sides the unknown and 1/2", plus the now-known hypoteneuse. So use the Pythagorean Theorem again and you're done!