A square contains a red rectangle with an extended side. Prove that red=|AB||AC|+|BE||CD|. By Matthew Arcus.
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Solution
![](https://mirangu.com/wp-content/uploads/2024/04/SquaringARectangle2Solution1.jpg)
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
![](https://mirangu.com/wp-content/uploads/2024/04/SquaringARectangle2Solution2.jpg)
Video
Please find here the video solution: Video: Squaring a rectangle II.