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Pythagorean theorem challenge

Ryan is putting a clothesline in his rectangular backyard. He wants to put it between two trees on the edge of his property. He has measured his property, and made the sketch shown below, where all the lengths listed are in meters.
What is the smallest length of rope that Ryan could buy which would stretch from one tree to the other?
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
meters