A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try?
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Draw or Cut two similar squares with sides units long.
Draw or cut four pairs of similar right triangles with side lengths as indicated in the diagram.
Now arrange the similar triangles at the corners of the squares such that the sides of one similar triangle plus the side
of a second similar triangle coincides with the length of the square.
We do another arrangement of the similar triangles. This time arrange another 4 similar triangles in the opposite corners, such that each pair forms a square.
Now comparing the two different arrangements we got two different areas that are equal.
The area of the uncovered squares in the first arrangement is
The area of the two uncovered squares in the second arrangement is
Equating the two areas gives the Pythagoras Theorem
Note that is the hypotenuse,
and
are two shorter sides of the similar right triangles.
