Use the babylonian method of false position to solve the following
problem,
taken from a clay tablet found in susa: let the width of a
rectangle measure a
quarter less than the length. let 40 be the length of the diagonal.
what are
the length and width? begin with the assumption that 1 (or 60) is
the length
of the rectangle.

Step-by-step explanation:

Assume a solution

Assume that 60 is the length. The width is then 1/4 less, or 60 -60/4 = 45.

The diagonal of this rectangle is found using the Pythagorean theorem:

  d = √(60² +45²) = √5625 = 75

Make the adjustment

This is a factor of 75/40 larger than the actual diagonal, so the actual dimensions must be 40/75 = 8/15 times those we assumed.

  length = (8/15)×60 = 32

  width = (8/15)×45 = 24

The length and width of the rectangle are 32 and 24, respectively.

Comment on this solution method

This method is suitable for problems where variables are linearly related. If we were concerned with the area, for example, instead of the diagonal, we would have to adjust the linear dimensions by the square root of the ratio of desired area to "false" area.

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