



 
Hi Chris, If you cut a triangle off each corner to form a regular octagon then my diagram would be You don't know the lengths $x$ or $y$ but you do know that $x + y + x = 30$ inches. The key step here is Pythagoras' Theorem. The triangle $ABC$ is a right triangle so Pythagoras' Theorem saya that the length of the side $BC$, $BC$ is given by \[BC^2 = CA^2 + AB^2 = x^2 + x^2 = 2x^2.\] But $BC = y$ so, since $x + y + x = 30$ we know that \[x + \sqrt{2 x^2} + x = 30 \mbox{ or } x + \sqrt{2} x + x = 30\] or \[x = \frac{30}{2 + \sqrt{2}} = 8.79 \mbox{ inches.}\] I hope this helps,  


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