Experiment with the sliders to change the width and height of this right-angled triangle.[br]Watch what happens to the areas of the squares.[br][br]What do you notice?[br][br]How might that let you predict the length of the longest side [i]c[/i] (the [i]hypotenuse[/i]) from the width [i]a[/i] and height [i]b[/i] ?

If you set the width to 8 and height to 6, what will the three square areas be?[br]So what length will the hypotenuse [i]c[/i] be in this triangle?[br][br]The sliders won't allow it, but suppose I could set a width [i]a[/i] = 12 and height [i]b[/i] = 5. What would the hypotenuse [i]c[/i] be now? Why?[br][br]What if I set [i]a[/i] = 7 and [i]b[/i] = 24?[br][br]Can you write a general rule about how [i][b]c[/b][/i] is connected to [i][b]a[/b][/i] and [i][b]b[/b][/i]?[br]Can you write that rule in algebra?