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Hypotenuse of big triangle: \(\sqrt{13}\)
This is just a compilation of a bunch of equations!
By Pythagorean Theorem:
(1) \((2-b)^2+(3-d)^2=b^2-a^2\)
(2) \(b^2-a^2=d^2-c^2\)
(3) \(d^2-c^2=\sqrt{13}-a-c\)
By similarity where \(s\) is the side length of the square:
(4) \(\frac{a}{b}=\frac{d}{s}\)
(5) \(\frac{2}{3}=\frac{2-b}{3-d}\)
(6) \(\frac{2}{3}=\frac{s}{c}\)
(7) \(\frac{2}{3}=\frac{a}{s}\)
General:
(8) \(a+c+s=\sqrt{13}\)
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