Babylonian Mathematics/Examples/Sum of Squares

Example of Babylonian Mathematics
An area $A$, consisting of the sum of $2$ squares, is $1000$.

The side of one square is $10$ less than $\dfrac 2 3$ of the other square.

What are the sides of the squares?

Solution
The lengths of the sides of the $2$ squares are $10$ and $30$.

Proof
Let $x$ be the length of the side of the smaller square.

Let $y$ be the length of the side of the larger square.

Thus:

We can dispose of the negative value, leaving us with:

and we see that:

as required.