Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door. It is found that the rod is 4 feet longer than the width of the door, two feet longer than the height and the same length as the diagonal. What are the dimensions of the door?

*Jiuzhang Suanshu* (*The Nine Chapters on the Mathematical Art*), c. 100 BCE

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The answer is: 6ft by 8ft