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How do you solve for $x$ for this triangle?

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The $1$m square is enclosed by the triangle, which is not a side length of the triangle - that's why I'm having trouble.

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    is this a square inscribed in a triangle? – 2017-01-29
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    Yeah that's right so thats why i don't think i could use pythagoras' theorem – 2017-01-29
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    and what side has the length of $1m$? – 2017-01-29
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    Oh yeah the yellow box is a cube – 2017-01-29

2 Answers 2

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Use the fact that you have two congruent triangles, so the proportion between the sides should be identical $\frac{\sqrt{(x-1)^2+1^2}}{x-1}=\frac{10}{x}$. Solving the equation can be done with a calculator or computer.

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    When you say "solving should not be too hard", note that squaring gives you a quartic. – 2017-01-29
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    I didn't immediately think of that, thanks, but I assume you can use some sort of calculator since the answer won't be a nicely rounded number. – 2017-01-29
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    This kind of problem (ladder against wall) quite often generates a quartic, so unless there is an obvious case-dependent trick or root it will not be so easy seems. – 2017-01-29
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If the yellow rectangle is not a square, then his side =1 means nothing (except that the base is larger than 1), and there is no single solution.

Otherwise, you have 3 triangles with the same proportions, and you know 1 side of each triangle (1 with base=1, 1 with height=1, and 1 triangle with diagonal=10)

Dr. Sonnhard Graubner gave you the answer when y is the base of the smallest triangle.