Question 198847
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Since it is a square, the triangle formed by two adjacent sides of the square and the diagonal is an isosceles right triangle -- observation confirmed by the fact that you say it is a 90°-45°-45° triangle.  All isosceles right triangles are similar, that is to say that their sides are in proportion.


If you have an isosceles right triangle whose legs measure 1 unit, then the Pythagorean Theorem says the hypotenuse is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c = \sqrt{1^2+1^2} = \sqrt{2}]


That means that the three sides of any isosceles right triangle are in proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1:1:\sqrt{2}]


So, if your hypotenuse, i.e. the diagonal of the square, measures *[tex \Large 6\sqrt{2}], then the two legs must each measure 6 because


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6:6:6\sqrt{2}]


is equivalent to


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1:1:\sqrt{2}]


Can you take it from there?


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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