document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195700>Question 195700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are two similar right triangles.<BR>\n" );
document.write( "The larger triangles hypotenuse is 15 and a leg is 3x, and the other is 3x+3. The smaller triangle has a hypotenuse of 5 one leg is x and the other is x+1.\r<BR>\n" );
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document.write( "How would you write an equation expressing the relationship among the length of the sides of the triangles for the smaller and the larger triangle?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146813 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=146813\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two similar right angled triangles.\r<BR>\n" );
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document.write( "The larger triangles hypotenuse is 15 and a leg is 3x, and the other is 3x+3. The smaller triangle has a hypotenuse of 5 one leg is x and the other is x+1.\r<BR>\n" );
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document.write( "How would you write an equation expressing the relationship among the length of the sides of the triangles for the smaller and the larger triangle?\r<BR>\n" );
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document.write( "Going by Pythagoras’ Theorem, the square on the hypotenuse is equal to the sum of the squares of the other two sides, which means:\r<BR>\n" );
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document.write( "For the larger triangle, 15^2 = (3x)^2 + (3x+3)^2\r<BR>\n" );
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document.write( "225 = 9x^2 + 9x^2 + 18x + 9 = 18x^2 + 18x + 9 = 9 (2x^2 + 2x + 1)\r<BR>\n" );
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document.write( "25 = 2x^2 + 2x + 1 (cancelling by 9)\r<BR>\n" );
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document.write( "giving 0 = 2x^2 + 2x – 24\r<BR>\n" );
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document.write( "and then 0 = x^2 + x – 12 (cancelling by 2)\r<BR>\n" );
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document.write( "We are left with x^2 + x – 12 = 0 = (x + 4)(x – 3) giving x = 3 or -4 but we cannot have a negative length, so the solution is x = 3 units whatever the units are.\r<BR>\n" );
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document.write( "This is the same solution for the smaller triangle since they are similar triangles and every factor has been scaled down by a factor of 3 squared (9) as 3 is the ratio of the larger triangle to the smaller triangle. We would have arrived at 25 = 2x^2 + 2x + 1 without cancelling by 9 if we did to the small triangle what we did to the large triangle.\r<BR>\n" );
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document.write( "So the sides of the triangles are:\r<BR>\n" );
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document.write( "Large: 15, 3x and 3x + 3 giving 15, 9 and 12\r<BR>\n" );
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document.write( "Small: 5, x and x + 1 giving 5, 3 and 4. </SPAN>\n" );
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