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Home Q & A Board Science-Related Homework Help Mathematics
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micaht25 micaht25
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10 years ago
inscribed square to that of the larger square?

The four vertices of the inscribed square lie on the four sides of the larger square.

I got the smallest ratio to be that of 1/2, but I am not sure as how to do a proof for it. Please help thank you!
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#1
10 years ago
If one side of the larger square is S and that side is split into two parts by the vertex of the inscribed square with part a being anti-clockwise of the inscribed square and part b being the part clockwise from the inscribed square, then one side of the inscribed square is the hypotenuse of the triangle formed by the legs (a) and (b) thus making the area of the inscribed square:

A = S²/4 + (S/2)²]/S² = (S²/4 + S²/4)/S² = (S²/2)/S² = 1/2
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