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Math Help - Polygons Help!

  1. #1
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    Exclamation Polygons Help!

    Okay, I've posted after a long time, I know... But I'm here with another doubt.
    The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

    Thanks!
    Last edited by Ruler of Hell; January 6th 2007 at 06:34 AM.
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  2. #2
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    Quote Originally Posted by Ruler of Hell View Post
    Okay, I've posted after a long time, I know... But I'm here with another doubt.
    The ratio between the sides of 2 regular polygons is 4 : 5 and the ratio between the interior angles is 15 : 16. Find the number of sides.

    Thanks!
    Let the number of sides of the polygons be n and m, then the first condition tell you that:

    \frac{n}{m}=\frac{4}{5}\ \ \ \dots(1) ,

    and as the interior angle of a ploygon with n sides is 180(n-2)/n, the second condition tells us that:

    <br />
\frac{n-2}{n}\,\frac{m}{m-2}=\frac{15}{16}<br />

    which may be simplified as we know n/m=4/5 to:

    <br />
\frac{n-2}{m-2}=\frac{3}{4}\ \ \ \dots(2) <br />

    Now we can proceed to solve (1) and (2), or we can just guess, when we find n=8, m=10.

    RonL
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  3. #3
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    Wait, I'm still a li'l confused. How did you solve equation 1 and 2? Sorry....
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  4. #4
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    Quote Originally Posted by Ruler of Hell View Post
    Wait, I'm still a li'l confused. How did you solve equation 1 and 2? Sorry....
    I guessed, n and m have to be integers so I tried n=4, m=5 and that didn't
    work so then I tried n=8, m=10 which did work. Also the solution is obviously
    unique, so n=8, m=10 is the only solution.

    RonL
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  5. #5
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    Got it! Yay, thanks a tonne Captain Black... (Though I used 2 different methods, yours and another one) Nonetheless, thanks!
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