Side length of a square in a squared rectangle I have a squared rectangle where I want to find the side length of a sub-square (for the record, consult the omniscient Google).

Here's what I've already done.
$$14 + 4 + x = \mathrm{height}.$$
The teeny square has a side length of 1.
If the square to the right of the tiny square has side length $a$, $$x = 9 + a - 1.$$ This problem would be a lot easier if the rectangle were a square (if you think it is, prove it), but I'm not sure what to do now.

We do some side-chasing.
The square below the $14$ is $10\times 10$.
So the square to the right of that is $7\times 7$. (Here the fact that the teeny square is $1\times 1$ is used.)
The square to the right of the $9$ is $8\times 8$.
So the mystery square has side $7+8$.
