# Discovering Pythagoras' Theorem

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- mathsurgery.wikispaces

Experiment with the sliders to change the width and height of this right-angled triangle.
Watch what happens to the areas of the squares.
What do you notice?
How might that let you predict the length of the longest side

*c*(the*hypotenuse*) from the width*a*and height*b*?If you set the width to 8 and height to 6, what will the three square areas be?
So what length will the hypotenuse

*c*be in this triangle? The sliders won't allow it, but suppose I could set a width*a*= 12 and height*b*= 5. What would the hypotenuse*c*be now? Why? What if I set*a*= 7 and*b*= 24? Can you write a general rule about how*is connected to***c***and***a***? Can you write that rule in algebra?***b**