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← The Baudhayana-Pythagoras Theorem

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Lesson 5 of 16

Finding the long side

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6 min

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A store room is 9 m by 12 m. The diagonal runs from one corner to the opposite corner. You want its length before you cut any string. The short sides are the two that meet at the square corner.

Square both short sides and add: 81 + 144 = 225.
Step 1 of 4
  1. Square both short sides and add: 81 + 144 = 225.
  2. Hunt for a match: 15 × 15 = 225. The long side is 15.
  3. Try short sides of 2 and 3: 4 + 9 = 13.
  4. No whole number fits. 9 < 13 < 16, so the side is between 3 and 4.

The diagonal is 15 m. To hunt is to try numbers until one squares to the total.

Rule: Square both short sides and add them. The long side is the number that squares to that total. It is not always a whole number.

Two more. Sides 7 and 24: 49 + 576 = 625, and 25 × 25 = 625. Sides 9 and 40: 81 + 1600 = 1681, and 41 × 41 = 1681.

Read the two short sides. Tap the long side.

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