bonanova Posted March 11, 2015 Report Share Posted March 11, 2015 What fraction of the black square does the red right triangle occupy? Quote Link to comment Share on other sites More sharing options...

0 gavinksong Posted March 11, 2015 Report Share Posted March 11, 2015 Applying the Pythagorean theorem on the right triangle formed from the circle's center and the red square's right side, 1 = R/4 + R where R is the area of the red square, gives us R = 4/5. The red triangle is a fourth of this: 1/5. Applying the Pythagorean theorem for the right triangle formed from a corner of the black square and a segment of the circle's diameter, 1 = B/4 + B/4 where B is the area of the black square, gives us B = 2. So the red triangle occupies a 10th of the black square. Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 11, 2015 Author Report Share Posted March 11, 2015 I had thought of making this a different problem: Given the black square (only) construct a shape inside the square that is 1/10 of its area. It would entail making the circumcircle, the red square inscribed in the upper semicircle (the hard part) and finally the two red diagonals. I wonder [1] if anyone would have gotten that solution or [2] if there is a simpler way. Quote Link to comment Share on other sites More sharing options...

0 gavinksong Posted March 11, 2015 Report Share Posted March 11, 2015 I had thought of making this a different problem: Given the black square (only) construct a shape inside the square that is 1/10 of its area. It would entail making the circumcircle, the red square inscribed in the upper semicircle (the hard part) and finally the two red diagonals. I wonder [1] if anyone would have gotten that solution or [2] if there is a simpler way. I agree. That would have been a much harder problem. I probably wouldn't have been able to solve it. I didn't realize this was an original puzzle. Good job! Quote Link to comment Share on other sites More sharing options...

0 bonanova Posted March 12, 2015 Author Report Share Posted March 12, 2015 Well I found the image. But then what kind of puzzle to make of it? Quote Link to comment Share on other sites More sharing options...

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What fraction of the black square does the red right triangle occupy?

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