Maths · Rung 17 of 30

Pythagoras

In a right triangle, the square of the hypotenuse (the longest side, opposite the right angle) is the sum of the squares of the legs: a² + b² = c². With 3 and 4, c = √(9 + 16) = 5.

Where this sits

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Exercises from this rung

Generated by the app, from easiest to hardest

  1. What is the perimeter of the triangle?

    • 30
    • 34
    • 17
    • 31

    Why The hypotenuse is √(5² + 12²) = 13. Perimeter: 5 + 12 + 13 = 30.

    easier

  2. How long is the hypotenuse x?

    • 21
    • 14
    • 16
    • 15

    Why x² = 9² + 12² = 81 + 144 = 225, so x = √225 = 15. Not 9 + 12: the sides do not add, their squares do.

    in between

  3. How long is leg x?

    • 8
    • 32
    • 2
    • 15

    Why x² = 17² − 15² = 289 − 225 = 64, so x = √64 = 8.

    harder