What is the theory of Pythagoras?

Answer 1

The Pythagoras theorem is used to find the longest side of a right angled triangle (2D form) or the longest diagonal that can fit in a cuboid (3D form). The 2D form is this:

If you have a right angled triangle then you call the longest side c and the shorter sides a and b. The Pythagoras theorem says that a^2 + b^2 = c^2 .

eg. say you have a right angled triangle and the two short sides a 3 and 4 cm, then you know that as a^2 + b^2 = c^2, 3^2 + 4^2 = c^2 so 9 + 16 = d^2 so 25 = d^2 and then you know that d, the longest side of the right anlged triangle, is 5 (the square root of 25)

The 3D form is that if you have a cuboid (rectangular prism) and you call the length a, the width b, the height c and the longest diagonal that can fit in the box d then a^2 + b^2 + c^2 = d^2

eg. say you have a cuboid with a length of 3 cm, a width of 4 cm and a height of 12 cm then you know that as a^2 + b^2 + c^2 = d^2, 3^2 + 4^2 + 12^2 = d^2 so 9 + 16 + 144 = d^2 so 169 = d^2 so 13 = d (13 is the square root of 169)

Hope this helped!