(adsbygoogle = window.adsbygoogle || []).push({}); simple math i can't figure out!!

so i'm trying to do this chemistry problem...i have the answer, but for some reason i can't do the math myself... ive taken calculus but for some reason i just can't get this!

i have from my answer sheet:

(2 R)^2 + (2√2 R)^2 = (2 r + 2 R)^2

therefore

(√3 -1) R = r

r/R = √3 -1 = 0.73

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i cannot seem to figure out how to get to r/R ???

when i do the math, i get

4R^2 +8R^2= 4R^2+ 4Rr+ 4Rr+4r^2

which i simplify to

8R^2=8Rr+4r^2

then to 2R^2= 2Rr+r^2

then what?? where on earth does √3 -1 come from???

please help!

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# Homework Help: Simple math i can't figure out

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