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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)?

11 answers

If the semicircles have a diameter of 10, then the square inside the platter has side 10.

So, the platter has a total width of 5+10+5 = 20

So, the enclosing square has a side of 20.
dude steave ur wrong the answer has to be a square root...
The middle part is sqrt(50) and the other parts are the radius, whitch is 5 so the answer is 10+sqrt(50)
oh I forgot that simplifies to 10+5*sqrt(2)
Tiger, maybe that would have been helpful a year ago :/ (cough cough)
No GaMinG
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.
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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var html = "<img src = '"+url+"' />"
document.getElementById("1881457").innerHTML = html;
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Didn't work...too bad
sTOP chEATINGgggg
jk cheating is cool and we encourage
No