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

diagram

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.

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    $\begingroup$ Just detective work, real quick. It is $7+8$ $\endgroup$ Jul 17, 2014 at 3:57
  • $\begingroup$ @AndréNicolas Could you explain (or hint at) that in an answer? $\endgroup$ Jul 17, 2014 at 3:59
  • $\begingroup$ Done, I hope what I wrote is clear. Unfortunately, I cannot point online, and the squares are not labelled. $\endgroup$ Jul 17, 2014 at 4:03

2 Answers 2

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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 $7+8$.

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Follow these steps:

left middle square is 10, because 14-4
tiny square is 1, because 10-9
square below tiny is 8, because 9-1
square to the right of tiny is 7, because 8-1

x is 15, 7+8

The answer is
E) 15

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