Alicia has a flat platter shaped like a square with a semicircle of diameter 10 inches on each edge. What is the number of inches in the side length of the smallest square that can contain the platter
(which contains the square with the semicircles on each side of it)?
oh I forgot that simplifies to 10+5*sqrt(2)
Let the points of tangency of the semicircles GJ and IJ to AD and BC be T and U, respectivly. Since S and R are midpoint of a square with side length 10, we have SJ = 5 = RJ, so triangle SJR is a 45-45-90 triangle. Thus, SR = 5sqrt2. The side length of the square is
TU = TS + SR + RU = TS + 5sqrt2 + RU.
But TS and RU are both radii of semicircles GJ and IJ, respectivly, so TS = 5 = RU, and so TU = 5 + 5sqrt2 + 5 = 10 + 5sqrt2.
The middle part is sqrt(50) and the other parts are the radius, whitch is 5 so the answer is 10+sqrt(50)
dude steave ur wrong the answer has to be a square root...
sTOP chEATINGgggg
jk cheating is cool and we encourage
No
Didn't work...too bad
No GaMinG
Better formatted version (might not work--jiskha doesn't seem to have built-in support for images, so ignore this message if it doesn't work)
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