Revise Pythagoras' Theorem with Dan

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? Can you write an equation of that? 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 c is connected to a and b? Can you write that rule in algebra?