document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148864>Question 1148864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One square is placed on top of another so that a regular octagon is formed, along with eight isosceles triangles each with its hypotenuse on a side of the octagon. If the perimeter of the octagon is 20cm, find the perimeter of the star, in cm. \r<BR>\n" );
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document.write( "Diagram: https://imgur.com/a/C5NSnNK </SPAN>\n" );
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document.write( "In each of the isosceles right triangles, the hypotenuse is 1/8 of the perimeter of the octagon, which is 20/8 = 2.5cm.<br><BR>\n" );
document.write( "The sides of an isosceles right triangle are in the ratio 1:1:sqrt(2), so each leg of each isosceles triangle has a length 2.5/sqrt(2), or 1.25*sqrt(2).<br><BR>\n" );
document.write( "The perimeter of the star is the combined perimeter of both legs of all the isosceles triangles, which is 16*(1.25*sqrt(2)) = 20*sqrt(2).<br><BR>\n" );
document.write( "ANSWER: 20*sqrt(2) cm </SPAN>\n" );
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