Question 334845
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The diagonal of a square creates two isosceles right triangles with the diagonal of the square as the hypotenuse.  The three sides of an isosceles right triangle are in proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1:\frac{\sqrt2}{2}:\frac{\sqrt2}{2}]


Verification of this claim is left as an exercise for the student. (Hint: use Pythagoras with an isosceles triangle with hypotenuse of 1 and sides of *[tex \Large x])


Hence, if the diagonal of the square is 20, then the hypotenuse of the triangle is 20 and the side of the triangle must be *[tex \Large 10\sqrt{2}].


The area of a square is the measure of the side of the square squared.  So calculate:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(10\sqrt{2}\right)^2]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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