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Point X is randomly selected on the perimeter of a square of length $L$. $M$ is the midpoint of side. What is the probability that $XM> L$?

  1. $\frac{\sqrt 3 }{3}$
  2. $\frac{3 - \sqrt{3}}{3} $
  3. $\frac{3 - \sqrt{3}}{4}$
  4. $\frac{1+\sqrt{3}}{4}$

$OA$ is $C$. Please let me know the process.

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$M$ is the midpoint of which side? Does $M$ depend on $X$? –  Twiceler Mar 24 '13 at 20:04
Here's a tutorial and reference for how to format math on this site. Your question is currently close to unreadable. Also note that people are likely not to know all abbreviations that you use; writing things out costs you a couple of keystrokes but saves dozens and potentially hundreds of readers the time it takes to fathom the intended meaning. –  joriki Mar 24 '13 at 20:05
Not sure of what you want :s ... is there 5 question there? Can you clarify what exactly are the questions? And what do you mean by "$OA$ is $C$"? –  wece Mar 24 '13 at 20:17
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1 Answer


Let M be the midpoint of the bottom side.

  1. Where on the square must the point fall to have $XM \gt L$?
  2. What ratio is this region to the whole?
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