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A goat is tied to an external corner of a rectangular shed measuring 20m by 15m. If the goat's rope is 13m long, what is the total area of grass in square meters, the goat can graze on?

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    $\begingroup$ Welcome to MSE! Questions consisting of just a problem statement so that we can do your homework for you make people sad. Please think about Providing Context for your question, such as your own ideas about how to proceed, or what exactly you're having trouble with here. $\endgroup$ – Misha Lavrov Apr 11 '18 at 0:37
  • $\begingroup$ Possible duplicate of A goat tied to a corner of a rectangle $\endgroup$ – amd Apr 11 '18 at 4:45
  • $\begingroup$ The problem should have a second similar question but now with a 35 meters rope. $\endgroup$ – Jean Marie Apr 11 '18 at 20:56
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Is this what you mean by a rectangular shed? enter image description here

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  • $\begingroup$ THANKYOU SOOOOO MUCH!!!!!!!!!!!! $\endgroup$ – Olivia Apr 11 '18 at 1:47
  • $\begingroup$ [+1] for taking time to give a nice graphical explanation. $\endgroup$ – Jean Marie Apr 12 '18 at 5:02
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Hint

If you draw a picture of this region, we see that we get $3/4$ of a circle of radius $13$.

The physical reasoning behind this can be seen if we think about how the rope is being used in this sense. Tie it to one end and stretch it out to its max length, then if we want to keep the rope tight, we can only move in a circle. And since the rope is $13$ meters long while the sides of the shed are $15$ and $20$ meters, we cannot go around another corner of the shed.

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