Rthur’s mother is a mechanical engineer. She is designing rectangular carts for moving finished goods from a factory’s manufacturing floor to the loading dock, where the goods are placed on trucks. She made a drawing showing where the carts must turn from a hallway 48 inches wide to pass through a doorway 36 inches wide. The drawing shows the longest cart that will pass through the doorway.

A 48 inches wide rectangular hallway with 30 inches wide doorway leading to the manufacturing floor and 36 inches wide doorway leading to the loading dock is given. A cart BCDE has been tilted slightly to pass through the 36 inches wide doorway. A dotted line from C to a point A on the opposite side of the cart and another dotted line from D to a point F on the line AC are drawn. The angle between A and F is 90 degrees. One more dotted line from E extends to a point G on the wall forming a triangle GED.

Part A
Triangles ΔABC and ΔCFD are triangles.