A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.

Solution

AB:AF=AD:AC, AB×AC=AD×AF
BE:BG=AD:CD, BE×CD=AD×BG
∴ AB×AC+BE×CD=AD×(AF+BG)
∵ AD=AH, AF+BG=AI,
∴ AB×AC+BE×CD=AH×AI=red

Video

Please find here the video solution: Video: Squaring a rectangle II.

A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By @MatthewArcus pic.twitter.com/lumQcATmz0

— Mirangu (@Mirangu1) March 29, 2024