Babylonian Problem Solving

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We look at some problems the Ancient Babylonians solved.

Here are two examples of problems the Ancient Babylonians solved. For each problem, do the following:

(a): Follow the procedure to get the answer, check each step along the way, and check that it’s the right answer!
(b): Determine what the underlying method is. Will it work for other kinds of problems?
(c): Draw some pictures to illustrate your solution method.

The area and two thirds of the side of my square I have added and it is $0;35$ . $1$ , the unit, you take. Two thirds of $1$ is $0;40$ : its half $0;20$ and $0;20$ you multiply by itself; $0;6,40$ , you add $0;35$ to it and $0;41,40$ has $0;50$ for its square root. $0;20$ that you multiplied with itself, from $0;50$ you subtract and $0;30$ is the side of the square.

I have multiplied length and width, obtaining the area $3,30$ . I add the length and width, $29$ . One follows this method. Take half of $29$ , $14;30$ . Square $14;30$ and get $3,30;15$ . Subtract $3,30$ from $3,30;15$ , you get $0;15$ . The square root of $0;15$ is $0;30$ . Add and subtract it from the other, you get the length $15$ and the width $14$ .