Puzzle #100: The 100 square rug puzzle (Prize Puzzle)!

Never imagined when I started 2 years back that I will be posting 100 puzzles at some time…thanks to all readers for continuous engagement and encouragement! Here goes the 100th one…will reveal the original source when I post the answer. I heard this puzzle through Alok Mittal’s Mathematical Circles class. First person to send back the correct answer gets a prize – children from Alok’s classes are not qualified as they have done this puzzle already!

When Nuriya Saradzheva was an adolescent, she was awarded a beautiful Turkmenian rug for being first on her collective farm to use an improved method of picking cotton. The rug was 12 feet by 9 feet in dimensions.

Now Nuriya works as an agronomist. Once, while doing her research, she spilled acid on the rug. After the damaged part was cut out, there was a large rectangular hole, 1 feet x 8 feet.

Nuriya decided to repair the rug. Using straight line cuts, she cut the undamaged part of the rug into 2 parts that, when sewn together, formed a square – 10 feet by 10 feet.

Puzzle 100 graphic

Puzzle 100 graphic

How?

As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.

Happy repairing!

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