🎮 How Long Is the Missing Side?

📖 About this game

A game on the Pythagorean theorem, whose text says that in a right triangle the square of the hypotenuse equals the sum of the squares of the two legs. The book two worked examples sit side by side under the heading finding a missing length, the first finding the hypotenuse from the legs and the second finding a leg from the hypotenuse and the other leg, and that is why five rounds ask for the hypotenuse and five for a leg: a learner who memorised add the two squares does not know the theorem and falls the moment he is given the hypotenuse. The three distractors are computed from the same triple and each one means something: working on the lengths instead of their squares, which is the commonest error in the chapter; forgetting the square root so the square remains; and the longer of the two known sides, which is what the book own reasonableness check measures, since the hypotenuse is always the longest side of a right triangle. The drawing is built from the lengths at one scale, and which leg is vertical and which is unknown is shuffled every round so the position of the answer cannot be memorised. The arithmetic proof, square then square then sum then root, is a clue that gives the answer away, so it is hidden in the question and shown after the tap. Ten triangles. No sign-up.

🕹️ How to play

1. Look at the triangle: which sides are known and which is missing?
2. For a missing hypotenuse add the two squares; for a missing leg subtract.
3. Take the square root, then tap the length you reached.
4. Every triangle you get first try counts for you.